forked from matplotlib/matplotlib.github.com
-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathmlab_api.html
More file actions
1355 lines (1305 loc) · 106 KB
/
mlab_api.html
File metadata and controls
1355 lines (1305 loc) · 106 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>matplotlib.mlab — Matplotlib 3.1.3 documentation</title>
<link rel="stylesheet" href="../_static/mpl.css?v3.1.3-2-g782f6ef56"
type="text/css" />
<link rel="stylesheet" href="../_static/pygments.css"
type="text/css" />
<link rel="stylesheet" href="../_static/graphviz.css" type="text/css" />
<link rel="stylesheet" href="../_static/gallery.css" type="text/css" />
<link rel="stylesheet" href="../_static/copybutton.css" type="text/css" />
<script type="text/javascript" id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script>
<script type="text/javascript" src="../_static/jquery.js"></script>
<script type="text/javascript" src="../_static/underscore.js"></script>
<script type="text/javascript" src="../_static/doctools.js"></script>
<script type="text/javascript" src="../_static/language_data.js"></script>
<script type="text/javascript" src="../_static/clipboard.min.js"></script>
<script type="text/javascript" src="../_static/copybutton.js"></script>
<script type="text/javascript">var copybuttonSkipText = '>>> ';</script>
<script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="search" type="application/opensearchdescription+xml"
title="Search within Matplotlib 3.1.3 documentation"
href="../_static/opensearch.xml"/>
<link rel="shortcut icon" href="../_static/favicon.ico"/>
<link rel="index" title="Index" href="../genindex.html"
/>
<link rel="search" title="Search" href="../search.html"
/>
<link rel="top" title="Matplotlib 3.1.3 documentation" href="../index.html" />
<link rel="up" title="API Overview" href="index.html" />
<link rel="next" title="matplotlib.offsetbox" href="offsetbox_api.html" />
<link rel="prev" title="matplotlib.mathtext" href="mathtext_api.html" />
<link rel="canonical" href="https://matplotlib.org/3.1.3/api/mlab_api.html" />
</head>
<body>
<div style="background-color: white; text-align: left; padding: 10px 10px 15px 15px; position: relative;">
<a href="../index.html">
<div style="float: left; position: absolute; width: 496px; bottom: 0; padding-bottom: 24px"><span style="float: right; color: #789; background: white">Version 3.1.3</span></div>
<img src="../_static/logo2_compressed.svg" height="125px" border="0" alt="matplotlib"/></a>
<!-- The "Fork me on github" ribbon -->
<div id="forkongithub"><a href="https://github.com/matplotlib/matplotlib">Fork me on GitHub</a></div>
</div>
<nav class="main-nav">
<ul>
<li><a href="../users/installing.html">Installation</a></li>
<li><a href="../contents.html">Documentation</a></li>
<li><a href="../gallery/index.html">Examples</a></li>
<li><a href="../tutorials/index.html">Tutorials</a></li>
<li><a href="../devel/index.html">Contributing</a></li>
<li class="nav-right">
<form class="search" action="../search.html" method="get">
<input type="text" name="q" aria-labelledby="searchlabel" placeholder="Search"/>
</form>
</li>
</ul>
</nav>
<div class="related">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="../genindex.html" title="General Index"
accesskey="I">index</a></li>
<li class="right" >
<a href="../py-modindex.html" title="Python Module Index"
>modules</a> |</li>
<li class="right" >
<a href="offsetbox_api.html" title="matplotlib.offsetbox"
accesskey="N">next</a> |</li>
<li class="right" >
<a href="mathtext_api.html" title="matplotlib.mathtext"
accesskey="P">previous</a> |</li>
<li><a href="../index.html">home</a>| </li>
<li><a href="../contents.html">contents</a> »</li>
<li><a href="index.html" accesskey="U">API Overview</a> »</li>
</ul>
</div>
<div class="sphinxsidebar">
<div class="sphinxsidebarwrapper">
<h3><a href="../contents.html">Table of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#"><code class="docutils literal notranslate"><span class="pre">matplotlib.mlab</span></code></a><ul>
<li><a class="reference internal" href="#spectral-functions">Spectral functions</a></li>
</ul>
</li>
</ul>
<div class="relations">
<h3>Related Topics</h3>
<ul>
<li><a href="../contents.html">Documentation overview</a><ul>
<li><a href="index.html">API Overview</a><ul>
<li>Previous: <a href="mathtext_api.html" title="previous chapter"><code class="docutils literal notranslate"><span class="pre">matplotlib.mathtext</span></code></a></li>
<li>Next: <a href="offsetbox_api.html" title="next chapter"><code class="docutils literal notranslate"><span class="pre">matplotlib.offsetbox</span></code></a></li>
</ul></li>
</ul></li>
</ul>
</div>
<div id="sidebar-pagesource" role="note" aria-label="source link"
style="margin-top: 1.5em; padding-top: 0.1em; border-top: 1px solid #86989b">
<a href="../_sources/api/mlab_api.rst.txt"
style="color: #c0c0c0" rel="nofollow">Show Page Source</a>
</div>
</div>
</div>
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body">
<div class="section" id="module-matplotlib.mlab">
<span id="matplotlib-mlab"></span><h1><code class="docutils literal notranslate"><span class="pre">matplotlib.mlab</span></code><a class="headerlink" href="#module-matplotlib.mlab" title="Permalink to this headline">¶</a></h1>
<p>Numerical python functions written for compatibility with MATLAB
commands with the same names. Most numerical python functions can be found in
the <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/index.html#module-numpy" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy</span></code></a> and <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/index.html#module-scipy" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy</span></code></a> libraries. What remains here is code for performing
spectral computations.</p>
<div class="section" id="spectral-functions">
<h2>Spectral functions<a class="headerlink" href="#spectral-functions" title="Permalink to this headline">¶</a></h2>
<dl class="docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.cohere" title="matplotlib.mlab.cohere"><code class="xref py py-obj docutils literal notranslate"><span class="pre">cohere</span></code></a></dt>
<dd>Coherence (normalized cross spectral density)</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.csd" title="matplotlib.mlab.csd"><code class="xref py py-obj docutils literal notranslate"><span class="pre">csd</span></code></a></dt>
<dd>Cross spectral density using Welch's average periodogram</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend" title="matplotlib.mlab.detrend"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend</span></code></a></dt>
<dd>Remove the mean or best fit line from an array</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.psd" title="matplotlib.mlab.psd"><code class="xref py py-obj docutils literal notranslate"><span class="pre">psd</span></code></a></dt>
<dd>Power spectral density using Welch's average periodogram</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.specgram" title="matplotlib.mlab.specgram"><code class="xref py py-obj docutils literal notranslate"><span class="pre">specgram</span></code></a></dt>
<dd>Spectrogram (spectrum over segments of time)</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.complex_spectrum" title="matplotlib.mlab.complex_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">complex_spectrum</span></code></a></dt>
<dd>Return the complex-valued frequency spectrum of a signal</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.magnitude_spectrum" title="matplotlib.mlab.magnitude_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">magnitude_spectrum</span></code></a></dt>
<dd>Return the magnitude of the frequency spectrum of a signal</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.angle_spectrum" title="matplotlib.mlab.angle_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">angle_spectrum</span></code></a></dt>
<dd>Return the angle (wrapped phase) of the frequency spectrum of a signal</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.phase_spectrum" title="matplotlib.mlab.phase_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">phase_spectrum</span></code></a></dt>
<dd>Return the phase (unwrapped angle) of the frequency spectrum of a signal</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_mean" title="matplotlib.mlab.detrend_mean"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_mean</span></code></a></dt>
<dd>Remove the mean from a line.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_linear" title="matplotlib.mlab.detrend_linear"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_linear</span></code></a></dt>
<dd>Remove the best fit line from a line.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_none" title="matplotlib.mlab.detrend_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_none</span></code></a></dt>
<dd>Return the original line.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.stride_windows" title="matplotlib.mlab.stride_windows"><code class="xref py py-obj docutils literal notranslate"><span class="pre">stride_windows</span></code></a></dt>
<dd>Get all windows in an array in a memory-efficient manner</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.stride_repeat" title="matplotlib.mlab.stride_repeat"><code class="xref py py-obj docutils literal notranslate"><span class="pre">stride_repeat</span></code></a></dt>
<dd>Repeat an array in a memory-efficient manner</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.apply_window" title="matplotlib.mlab.apply_window"><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply_window</span></code></a></dt>
<dd>Apply a window along a given axis</dd>
</dl>
<dl class="class">
<dt id="matplotlib.mlab.GaussianKDE">
<em class="property">class </em><code class="descclassname">matplotlib.mlab.</code><code class="descname">GaussianKDE</code><span class="sig-paren">(</span><em>dataset</em>, <em>bw_method=None</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#GaussianKDE"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.GaussianKDE" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.8)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
<p>Representation of a kernel-density estimate using Gaussian kernels.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>dataset</strong> <span class="classifier-delimiter">:</span> <span class="classifier">array_like</span></dt>
<dd><p class="first last">Datapoints to estimate from. In case of univariate data this is a 1-D
array, otherwise a 2-D array with shape (# of dims, # of data).</p>
</dd>
<dt><strong>bw_method</strong> <span class="classifier-delimiter">:</span> <span class="classifier">str, scalar or callable, optional</span></dt>
<dd><p class="first last">The method used to calculate the estimator bandwidth. This can be
'scott', 'silverman', a scalar constant or a callable. If a
scalar, this will be used directly as <code class="xref py py-obj docutils literal notranslate"><span class="pre">kde.factor</span></code>. If a
callable, it should take a <a class="reference internal" href="#matplotlib.mlab.GaussianKDE" title="matplotlib.mlab.GaussianKDE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GaussianKDE</span></code></a> instance as only
parameter and return a scalar. If None (default), 'scott' is used.</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Attributes:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>dataset</strong> <span class="classifier-delimiter">:</span> <span class="classifier">ndarray</span></dt>
<dd><p class="first last">The dataset with which <code class="xref py py-obj docutils literal notranslate"><span class="pre">gaussian_kde</span></code> was initialized.</p>
</dd>
<dt><strong>dim</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int</span></dt>
<dd><p class="first last">Number of dimensions.</p>
</dd>
<dt><strong>num_dp</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int</span></dt>
<dd><p class="first last">Number of datapoints.</p>
</dd>
<dt><strong>factor</strong> <span class="classifier-delimiter">:</span> <span class="classifier">float</span></dt>
<dd><p class="first last">The bandwidth factor, obtained from <code class="xref py py-obj docutils literal notranslate"><span class="pre">kde.covariance_factor</span></code>, with which
the covariance matrix is multiplied.</p>
</dd>
<dt><strong>covariance</strong> <span class="classifier-delimiter">:</span> <span class="classifier">ndarray</span></dt>
<dd><p class="first last">The covariance matrix of <code class="xref py py-obj docutils literal notranslate"><span class="pre">dataset</span></code>, scaled by the calculated bandwidth
(<code class="xref py py-obj docutils literal notranslate"><span class="pre">kde.factor</span></code>).</p>
</dd>
<dt><strong>inv_cov</strong> <span class="classifier-delimiter">:</span> <span class="classifier">ndarray</span></dt>
<dd><p class="first last">The inverse of <code class="xref py py-obj docutils literal notranslate"><span class="pre">covariance</span></code>.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Methods</p>
<table border="1" class="docutils">
<colgroup>
<col width="27%" />
<col width="73%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><strong>kde.evaluate(points)</strong></td>
<td>(ndarray) Evaluate the estimated pdf on a provided set of points.</td>
</tr>
<tr class="row-even"><td><strong>kde(points)</strong></td>
<td>(ndarray) Same as kde.evaluate(points)</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="matplotlib.mlab.GaussianKDE.covariance_factor">
<code class="descname">covariance_factor</code><span class="sig-paren">(</span><em>self</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.GaussianKDE.covariance_factor" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.GaussianKDE.evaluate">
<code class="descname">evaluate</code><span class="sig-paren">(</span><em>self</em>, <em>points</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#GaussianKDE.evaluate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.GaussianKDE.evaluate" title="Permalink to this definition">¶</a></dt>
<dd><p>Evaluate the estimated pdf on a set of points.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>points</strong> <span class="classifier-delimiter">:</span> <span class="classifier">(# of dimensions, # of points)-array</span></dt>
<dd><p class="first last">Alternatively, a (# of dimensions,) vector can be passed in and
treated as a single point.</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first docutils">
<dt><strong>values</strong> <span class="classifier-delimiter">:</span> <span class="classifier">(# of points,)-array</span></dt>
<dd><p class="first last">The values at each point.</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Raises:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>ValueError</strong> <span class="classifier-delimiter">:</span> <span class="classifier">if the dimensionality of the input points is different</span></dt>
<dd><p class="first last">than the dimensionality of the KDE.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.GaussianKDE.scotts_factor">
<code class="descname">scotts_factor</code><span class="sig-paren">(</span><em>self</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#GaussianKDE.scotts_factor"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.GaussianKDE.scotts_factor" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.GaussianKDE.silverman_factor">
<code class="descname">silverman_factor</code><span class="sig-paren">(</span><em>self</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#GaussianKDE.silverman_factor"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.GaussianKDE.silverman_factor" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.angle_spectrum">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">angle_spectrum</code><span class="sig-paren">(</span><em>x</em>, <em>Fs=None</em>, <em>window=None</em>, <em>pad_to=None</em>, <em>sides=None</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#angle_spectrum"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.angle_spectrum" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the angle of the frequency spectrum (wrapped phase spectrum) of
<em>x</em>. Data is padded to a length of <em>pad_to</em> and the windowing function
<em>window</em> is applied to the signal.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>x</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array or sequence</span></dt>
<dd><p class="first last">Array or sequence containing the data</p>
</dd>
<dt><strong>Fs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">scalar</span></dt>
<dd><p class="first last">The sampling frequency (samples per time unit). It is used
to calculate the Fourier frequencies, freqs, in cycles per time
unit. The default value is 2.</p>
</dd>
<dt><strong>window</strong> <span class="classifier-delimiter">:</span> <span class="classifier">callable or ndarray</span></dt>
<dd><p class="first last">A function or a vector of length <em>NFFT</em>. To create window vectors see
<a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_hanning</span></code></a>, <a class="reference internal" href="#matplotlib.mlab.window_none" title="matplotlib.mlab.window_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_none</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.blackman.html#numpy.blackman" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.blackman</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.hamming.html#numpy.hamming" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.hamming</span></code></a>,
<a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.bartlett.html#numpy.bartlett" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.bartlett</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/signal.html#module-scipy.signal" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.signal</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.get_window.html#scipy.signal.get_window" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.signal.get_window</span></code></a>, etc. The
default is <a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_hanning</span></code></a>. If a function is passed as the argument,
it must take a data segment as an argument and return the windowed
version of the segment.</p>
</dd>
<dt><strong>sides</strong> <span class="classifier-delimiter">:</span> <span class="classifier">{'default', 'onesided', 'twosided'}</span></dt>
<dd><p class="first last">Specifies which sides of the spectrum to return. Default gives the
default behavior, which returns one-sided for real data and both
for complex data. 'onesided' forces the return of a one-sided
spectrum, while 'twosided' forces two-sided.</p>
</dd>
<dt><strong>pad_to</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int</span></dt>
<dd><p class="first last">The number of points to which the data segment is padded when
performing the FFT. While not increasing the actual resolution of
the spectrum (the minimum distance between resolvable peaks),
this can give more points in the plot, allowing for more
detail. This corresponds to the <em>n</em> parameter in the call to fft().
The default is None, which sets <em>pad_to</em> equal to the length of the
input signal (i.e. no padding).</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>spectrum</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array</span></dt>
<dd><p class="first last">The values for the angle spectrum in radians (real valued)</p>
</dd>
<dt><strong>freqs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array</span></dt>
<dd><p class="first last">The frequencies corresponding to the elements in <em>spectrum</em></p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.complex_spectrum" title="matplotlib.mlab.complex_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">complex_spectrum</span></code></a></dt>
<dd>This function returns the angle value of <a class="reference internal" href="#matplotlib.mlab.complex_spectrum" title="matplotlib.mlab.complex_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">complex_spectrum</span></code></a>.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.magnitude_spectrum" title="matplotlib.mlab.magnitude_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">magnitude_spectrum</span></code></a></dt>
<dd>Returns the magnitudes of the corresponding frequencies.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.phase_spectrum" title="matplotlib.mlab.phase_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">phase_spectrum</span></code></a></dt>
<dd>Returns the phase (unwrapped angle) of the corresponding frequencies.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.specgram" title="matplotlib.mlab.specgram"><code class="xref py py-obj docutils literal notranslate"><span class="pre">specgram</span></code></a></dt>
<dd>Can return the complex spectrum of segments within the signal.</dd>
</dl>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.apply_window">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">apply_window</code><span class="sig-paren">(</span><em>x</em>, <em>window</em>, <em>axis=0</em>, <em>return_window=None</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#apply_window"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.apply_window" title="Permalink to this definition">¶</a></dt>
<dd><p>Apply the given window to the given 1D or 2D array along the given axis.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>x</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1D or 2D array or sequence</span></dt>
<dd><p class="first last">Array or sequence containing the data.</p>
</dd>
<dt><strong>window</strong> <span class="classifier-delimiter">:</span> <span class="classifier">function or array.</span></dt>
<dd><p class="first last">Either a function to generate a window or an array with length
<em>x</em>.shape[<em>axis</em>]</p>
</dd>
<dt><strong>axis</strong> <span class="classifier-delimiter">:</span> <span class="classifier">integer</span></dt>
<dd><p class="first last">The axis over which to do the repetition.
Must be 0 or 1. The default is 0</p>
</dd>
<dt><strong>return_window</strong> <span class="classifier-delimiter">:</span> <span class="classifier">bool</span></dt>
<dd><p class="first last">If true, also return the 1D values of the window that was applied</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.cohere">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">cohere</code><span class="sig-paren">(</span><em>x</em>, <em>y</em>, <em>NFFT=256</em>, <em>Fs=2</em>, <em>detrend=<function detrend_none at 0x7f18a5ba4700></em>, <em>window=<function window_hanning at 0x7f18a5ba43a0></em>, <em>noverlap=0</em>, <em>pad_to=None</em>, <em>sides='default'</em>, <em>scale_by_freq=None</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#cohere"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.cohere" title="Permalink to this definition">¶</a></dt>
<dd><p>The coherence between <em>x</em> and <em>y</em>. Coherence is the normalized
cross spectral density:</p>
<div class="math notranslate nohighlight">
\[C_{xy} = \frac{|P_{xy}|^2}{P_{xx}P_{yy}}\]</div>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>x, y</strong></dt>
<dd><p class="first last">Array or sequence containing the data</p>
</dd>
<dt><strong>Fs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">scalar</span></dt>
<dd><p class="first last">The sampling frequency (samples per time unit). It is used
to calculate the Fourier frequencies, freqs, in cycles per time
unit. The default value is 2.</p>
</dd>
<dt><strong>window</strong> <span class="classifier-delimiter">:</span> <span class="classifier">callable or ndarray</span></dt>
<dd><p class="first last">A function or a vector of length <em>NFFT</em>. To create window vectors see
<a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_hanning</span></code></a>, <a class="reference internal" href="#matplotlib.mlab.window_none" title="matplotlib.mlab.window_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_none</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.blackman.html#numpy.blackman" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.blackman</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.hamming.html#numpy.hamming" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.hamming</span></code></a>,
<a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.bartlett.html#numpy.bartlett" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.bartlett</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/signal.html#module-scipy.signal" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.signal</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.get_window.html#scipy.signal.get_window" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.signal.get_window</span></code></a>, etc. The
default is <a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_hanning</span></code></a>. If a function is passed as the argument,
it must take a data segment as an argument and return the windowed
version of the segment.</p>
</dd>
<dt><strong>sides</strong> <span class="classifier-delimiter">:</span> <span class="classifier">{'default', 'onesided', 'twosided'}</span></dt>
<dd><p class="first last">Specifies which sides of the spectrum to return. Default gives the
default behavior, which returns one-sided for real data and both
for complex data. 'onesided' forces the return of a one-sided
spectrum, while 'twosided' forces two-sided.</p>
</dd>
<dt><strong>pad_to</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int</span></dt>
<dd><p class="first last">The number of points to which the data segment is padded when
performing the FFT. This can be different from <em>NFFT</em>, which
specifies the number of data points used. While not increasing
the actual resolution of the spectrum (the minimum distance between
resolvable peaks), this can give more points in the plot,
allowing for more detail. This corresponds to the <em>n</em> parameter
in the call to fft(). The default is None, which sets <em>pad_to</em>
equal to <em>NFFT</em></p>
</dd>
<dt><strong>NFFT</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int</span></dt>
<dd><p class="first last">The number of data points used in each block for the FFT.
A power 2 is most efficient. The default value is 256.
This should <em>NOT</em> be used to get zero padding, or the scaling of the
result will be incorrect. Use <em>pad_to</em> for this instead.</p>
</dd>
<dt><strong>detrend</strong> <span class="classifier-delimiter">:</span> <span class="classifier">{'none', 'mean', 'linear'} or callable, default 'none'</span></dt>
<dd><p class="first last">The function applied to each segment before fft-ing, designed to
remove the mean or linear trend. Unlike in MATLAB, where the
<em>detrend</em> parameter is a vector, in Matplotlib is it a function.
The <a class="reference internal" href="#module-matplotlib.mlab" title="matplotlib.mlab"><code class="xref py py-mod docutils literal notranslate"><span class="pre">mlab</span></code></a> module defines <a class="reference internal" href="#matplotlib.mlab.detrend_none" title="matplotlib.mlab.detrend_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_none</span></code></a>,
<a class="reference internal" href="#matplotlib.mlab.detrend_mean" title="matplotlib.mlab.detrend_mean"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_mean</span></code></a>, and <a class="reference internal" href="#matplotlib.mlab.detrend_linear" title="matplotlib.mlab.detrend_linear"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_linear</span></code></a>, but you can use a custom
function as well. You can also use a string to choose one of the
functions: 'none' calls <a class="reference internal" href="#matplotlib.mlab.detrend_none" title="matplotlib.mlab.detrend_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_none</span></code></a>. 'mean' calls <a class="reference internal" href="#matplotlib.mlab.detrend_mean" title="matplotlib.mlab.detrend_mean"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_mean</span></code></a>.
'linear' calls <a class="reference internal" href="#matplotlib.mlab.detrend_linear" title="matplotlib.mlab.detrend_linear"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_linear</span></code></a>.</p>
</dd>
<dt><strong>scale_by_freq</strong> <span class="classifier-delimiter">:</span> <span class="classifier">bool, optional</span></dt>
<dd><p class="first last">Specifies whether the resulting density values should be scaled
by the scaling frequency, which gives density in units of Hz^-1.
This allows for integration over the returned frequency values.
The default is True for MATLAB compatibility.</p>
</dd>
<dt><strong>noverlap</strong> <span class="classifier-delimiter">:</span> <span class="classifier">integer</span></dt>
<dd><p class="first last">The number of points of overlap between blocks. The default value
is 0 (no overlap).</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt>The return value is the tuple (<em>Cxy</em>, <em>f</em>), where <em>f</em> are the</dt>
<dd></dd>
<dt>frequencies of the coherence vector. For cohere, scaling the</dt>
<dd></dd>
<dt>individual densities by the sampling frequency has no effect,</dt>
<dd></dd>
<dt>since the factors cancel out.</dt>
<dd></dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.psd" title="matplotlib.mlab.psd"><code class="xref py py-func docutils literal notranslate"><span class="pre">psd()</span></code></a>, <a class="reference internal" href="#matplotlib.mlab.csd" title="matplotlib.mlab.csd"><code class="xref py py-func docutils literal notranslate"><span class="pre">csd()</span></code></a></dt>
<dd>For information about the methods used to compute <span class="math notranslate nohighlight">\(P_{xy}\)</span>, <span class="math notranslate nohighlight">\(P_{xx}\)</span> and <span class="math notranslate nohighlight">\(P_{yy}\)</span>.</dd>
</dl>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.complex_spectrum">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">complex_spectrum</code><span class="sig-paren">(</span><em>x</em>, <em>Fs=None</em>, <em>window=None</em>, <em>pad_to=None</em>, <em>sides=None</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#complex_spectrum"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.complex_spectrum" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the complex-valued frequency spectrum of <em>x</em>. Data is padded to a
length of <em>pad_to</em> and the windowing function <em>window</em> is applied to the
signal.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>x</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array or sequence</span></dt>
<dd><p class="first last">Array or sequence containing the data</p>
</dd>
<dt><strong>Fs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">scalar</span></dt>
<dd><p class="first last">The sampling frequency (samples per time unit). It is used
to calculate the Fourier frequencies, freqs, in cycles per time
unit. The default value is 2.</p>
</dd>
<dt><strong>window</strong> <span class="classifier-delimiter">:</span> <span class="classifier">callable or ndarray</span></dt>
<dd><p class="first last">A function or a vector of length <em>NFFT</em>. To create window vectors see
<a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_hanning</span></code></a>, <a class="reference internal" href="#matplotlib.mlab.window_none" title="matplotlib.mlab.window_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_none</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.blackman.html#numpy.blackman" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.blackman</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.hamming.html#numpy.hamming" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.hamming</span></code></a>,
<a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.bartlett.html#numpy.bartlett" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.bartlett</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/signal.html#module-scipy.signal" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.signal</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.get_window.html#scipy.signal.get_window" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.signal.get_window</span></code></a>, etc. The
default is <a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_hanning</span></code></a>. If a function is passed as the argument,
it must take a data segment as an argument and return the windowed
version of the segment.</p>
</dd>
<dt><strong>sides</strong> <span class="classifier-delimiter">:</span> <span class="classifier">{'default', 'onesided', 'twosided'}</span></dt>
<dd><p class="first last">Specifies which sides of the spectrum to return. Default gives the
default behavior, which returns one-sided for real data and both
for complex data. 'onesided' forces the return of a one-sided
spectrum, while 'twosided' forces two-sided.</p>
</dd>
<dt><strong>pad_to</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int</span></dt>
<dd><p class="first last">The number of points to which the data segment is padded when
performing the FFT. While not increasing the actual resolution of
the spectrum (the minimum distance between resolvable peaks),
this can give more points in the plot, allowing for more
detail. This corresponds to the <em>n</em> parameter in the call to fft().
The default is None, which sets <em>pad_to</em> equal to the length of the
input signal (i.e. no padding).</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>spectrum</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array</span></dt>
<dd><p class="first last">The values for the complex spectrum (complex valued)</p>
</dd>
<dt><strong>freqs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array</span></dt>
<dd><p class="first last">The frequencies corresponding to the elements in <em>spectrum</em></p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.magnitude_spectrum" title="matplotlib.mlab.magnitude_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">magnitude_spectrum</span></code></a></dt>
<dd>Returns the absolute value of this function.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.angle_spectrum" title="matplotlib.mlab.angle_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">angle_spectrum</span></code></a></dt>
<dd>Returns the angle of this function.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.phase_spectrum" title="matplotlib.mlab.phase_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">phase_spectrum</span></code></a></dt>
<dd>Returns the phase (unwrapped angle) of this function.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.specgram" title="matplotlib.mlab.specgram"><code class="xref py py-obj docutils literal notranslate"><span class="pre">specgram</span></code></a></dt>
<dd>Can return the complex spectrum of segments within the signal.</dd>
</dl>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.csd">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">csd</code><span class="sig-paren">(</span><em>x</em>, <em>y</em>, <em>NFFT=None</em>, <em>Fs=None</em>, <em>detrend=None</em>, <em>window=None</em>, <em>noverlap=None</em>, <em>pad_to=None</em>, <em>sides=None</em>, <em>scale_by_freq=None</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#csd"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.csd" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the cross-spectral density.</p>
<p>The cross spectral density <span class="math notranslate nohighlight">\(P_{xy}\)</span> by Welch's average
periodogram method. The vectors <em>x</em> and <em>y</em> are divided into
<em>NFFT</em> length segments. Each segment is detrended by function
<em>detrend</em> and windowed by function <em>window</em>. <em>noverlap</em> gives
the length of the overlap between segments. The product of
the direct FFTs of <em>x</em> and <em>y</em> are averaged over each segment
to compute <span class="math notranslate nohighlight">\(P_{xy}\)</span>, with a scaling to correct for power
loss due to windowing.</p>
<p>If len(<em>x</em>) < <em>NFFT</em> or len(<em>y</em>) < <em>NFFT</em>, they will be zero
padded to <em>NFFT</em>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>x, y</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D arrays or sequences</span></dt>
<dd><p class="first last">Arrays or sequences containing the data</p>
</dd>
<dt><strong>Fs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">scalar</span></dt>
<dd><p class="first last">The sampling frequency (samples per time unit). It is used
to calculate the Fourier frequencies, freqs, in cycles per time
unit. The default value is 2.</p>
</dd>
<dt><strong>window</strong> <span class="classifier-delimiter">:</span> <span class="classifier">callable or ndarray</span></dt>
<dd><p class="first last">A function or a vector of length <em>NFFT</em>. To create window vectors see
<a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_hanning</span></code></a>, <a class="reference internal" href="#matplotlib.mlab.window_none" title="matplotlib.mlab.window_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_none</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.blackman.html#numpy.blackman" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.blackman</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.hamming.html#numpy.hamming" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.hamming</span></code></a>,
<a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.bartlett.html#numpy.bartlett" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.bartlett</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/signal.html#module-scipy.signal" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.signal</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.get_window.html#scipy.signal.get_window" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.signal.get_window</span></code></a>, etc. The
default is <a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_hanning</span></code></a>. If a function is passed as the argument,
it must take a data segment as an argument and return the windowed
version of the segment.</p>
</dd>
<dt><strong>sides</strong> <span class="classifier-delimiter">:</span> <span class="classifier">{'default', 'onesided', 'twosided'}</span></dt>
<dd><p class="first last">Specifies which sides of the spectrum to return. Default gives the
default behavior, which returns one-sided for real data and both
for complex data. 'onesided' forces the return of a one-sided
spectrum, while 'twosided' forces two-sided.</p>
</dd>
<dt><strong>pad_to</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int</span></dt>
<dd><p class="first last">The number of points to which the data segment is padded when
performing the FFT. This can be different from <em>NFFT</em>, which
specifies the number of data points used. While not increasing
the actual resolution of the spectrum (the minimum distance between
resolvable peaks), this can give more points in the plot,
allowing for more detail. This corresponds to the <em>n</em> parameter
in the call to fft(). The default is None, which sets <em>pad_to</em>
equal to <em>NFFT</em></p>
</dd>
<dt><strong>NFFT</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int</span></dt>
<dd><p class="first last">The number of data points used in each block for the FFT.
A power 2 is most efficient. The default value is 256.
This should <em>NOT</em> be used to get zero padding, or the scaling of the
result will be incorrect. Use <em>pad_to</em> for this instead.</p>
</dd>
<dt><strong>detrend</strong> <span class="classifier-delimiter">:</span> <span class="classifier">{'none', 'mean', 'linear'} or callable, default 'none'</span></dt>
<dd><p class="first last">The function applied to each segment before fft-ing, designed to
remove the mean or linear trend. Unlike in MATLAB, where the
<em>detrend</em> parameter is a vector, in Matplotlib is it a function.
The <a class="reference internal" href="#module-matplotlib.mlab" title="matplotlib.mlab"><code class="xref py py-mod docutils literal notranslate"><span class="pre">mlab</span></code></a> module defines <a class="reference internal" href="#matplotlib.mlab.detrend_none" title="matplotlib.mlab.detrend_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_none</span></code></a>,
<a class="reference internal" href="#matplotlib.mlab.detrend_mean" title="matplotlib.mlab.detrend_mean"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_mean</span></code></a>, and <a class="reference internal" href="#matplotlib.mlab.detrend_linear" title="matplotlib.mlab.detrend_linear"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_linear</span></code></a>, but you can use a custom
function as well. You can also use a string to choose one of the
functions: 'none' calls <a class="reference internal" href="#matplotlib.mlab.detrend_none" title="matplotlib.mlab.detrend_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_none</span></code></a>. 'mean' calls <a class="reference internal" href="#matplotlib.mlab.detrend_mean" title="matplotlib.mlab.detrend_mean"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_mean</span></code></a>.
'linear' calls <a class="reference internal" href="#matplotlib.mlab.detrend_linear" title="matplotlib.mlab.detrend_linear"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_linear</span></code></a>.</p>
</dd>
<dt><strong>scale_by_freq</strong> <span class="classifier-delimiter">:</span> <span class="classifier">bool, optional</span></dt>
<dd><p class="first last">Specifies whether the resulting density values should be scaled
by the scaling frequency, which gives density in units of Hz^-1.
This allows for integration over the returned frequency values.
The default is True for MATLAB compatibility.</p>
</dd>
<dt><strong>noverlap</strong> <span class="classifier-delimiter">:</span> <span class="classifier">integer</span></dt>
<dd><p class="first last">The number of points of overlap between segments.
The default value is 0 (no overlap).</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>Pxy</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array</span></dt>
<dd><p class="first last">The values for the cross spectrum <code class="xref py py-obj docutils literal notranslate"><span class="pre">P_{xy}</span></code> before scaling (real valued)</p>
</dd>
<dt><strong>freqs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array</span></dt>
<dd><p class="first last">The frequencies corresponding to the elements in <em>Pxy</em></p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.psd" title="matplotlib.mlab.psd"><code class="xref py py-obj docutils literal notranslate"><span class="pre">psd</span></code></a></dt>
<dd>equivalent to setting <code class="docutils literal notranslate"><span class="pre">y</span> <span class="pre">=</span> <span class="pre">x</span></code>.</dd>
</dl>
</div>
<p class="rubric">References</p>
<p>Bendat & Piersol -- Random Data: Analysis and Measurement Procedures, John
Wiley & Sons (1986)</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.demean">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">demean</code><span class="sig-paren">(</span><em>x</em>, <em>axis=0</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#demean"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.demean" title="Permalink to this definition">¶</a></dt>
<dd><p>[<em>Deprecated</em>] Return x minus its mean along the specified axis.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>x</strong> <span class="classifier-delimiter">:</span> <span class="classifier">array or sequence</span></dt>
<dd><p class="first last">Array or sequence containing the data
Can have any dimensionality</p>
</dd>
<dt><strong>axis</strong> <span class="classifier-delimiter">:</span> <span class="classifier">integer</span></dt>
<dd><p class="first last">The axis along which to take the mean. See numpy.mean for a
description of this argument.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_mean" title="matplotlib.mlab.detrend_mean"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_mean</span></code></a></dt>
<dd>Same as <a class="reference internal" href="#matplotlib.mlab.demean" title="matplotlib.mlab.demean"><code class="xref py py-obj docutils literal notranslate"><span class="pre">demean</span></code></a> except for the default <em>axis</em>.</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<div class="deprecated">
<p><span class="versionmodified">Deprecated since version 3.1.</span></p>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.detrend">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">detrend</code><span class="sig-paren">(</span><em>x</em>, <em>key=None</em>, <em>axis=None</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#detrend"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.detrend" title="Permalink to this definition">¶</a></dt>
<dd><p>Return x with its trend removed.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>x</strong> <span class="classifier-delimiter">:</span> <span class="classifier">array or sequence</span></dt>
<dd><p class="first last">Array or sequence containing the data.</p>
</dd>
<dt><strong>key</strong> <span class="classifier-delimiter">:</span> <span class="classifier">[ 'default' | 'constant' | 'mean' | 'linear' | 'none'] or function</span></dt>
<dd><p class="first last">Specifies the detrend algorithm to use. 'default' is 'mean', which is
the same as <a class="reference internal" href="#matplotlib.mlab.detrend_mean" title="matplotlib.mlab.detrend_mean"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_mean</span></code></a>. 'constant' is the same. 'linear' is
the same as <a class="reference internal" href="#matplotlib.mlab.detrend_linear" title="matplotlib.mlab.detrend_linear"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_linear</span></code></a>. 'none' is the same as
<a class="reference internal" href="#matplotlib.mlab.detrend_none" title="matplotlib.mlab.detrend_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_none</span></code></a>. The default is 'mean'. See the corresponding
functions for more details regarding the algorithms. Can also be a
function that carries out the detrend operation.</p>
</dd>
<dt><strong>axis</strong> <span class="classifier-delimiter">:</span> <span class="classifier">integer</span></dt>
<dd><p class="first last">The axis along which to do the detrending.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_mean" title="matplotlib.mlab.detrend_mean"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_mean</span></code></a></dt>
<dd>Implementation of the 'mean' algorithm.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_linear" title="matplotlib.mlab.detrend_linear"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_linear</span></code></a></dt>
<dd>Implementation of the 'linear' algorithm.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_none" title="matplotlib.mlab.detrend_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_none</span></code></a></dt>
<dd>Implementation of the 'none' algorithm.</dd>
</dl>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.detrend_linear">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">detrend_linear</code><span class="sig-paren">(</span><em>y</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#detrend_linear"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.detrend_linear" title="Permalink to this definition">¶</a></dt>
<dd><p>Return x minus best fit line; 'linear' detrending.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>y</strong> <span class="classifier-delimiter">:</span> <span class="classifier">0-D or 1-D array or sequence</span></dt>
<dd><p class="first last">Array or sequence containing the data</p>
</dd>
<dt><strong>axis</strong> <span class="classifier-delimiter">:</span> <span class="classifier">integer</span></dt>
<dd><p class="first last">The axis along which to take the mean. See numpy.mean for a
description of this argument.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_mean" title="matplotlib.mlab.detrend_mean"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_mean</span></code></a></dt>
<dd>Another detrend algorithm.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_none" title="matplotlib.mlab.detrend_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_none</span></code></a></dt>
<dd>Another detrend algorithm.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend" title="matplotlib.mlab.detrend"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend</span></code></a></dt>
<dd>A wrapper around all the detrend algorithms.</dd>
</dl>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.detrend_mean">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">detrend_mean</code><span class="sig-paren">(</span><em>x</em>, <em>axis=None</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#detrend_mean"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.detrend_mean" title="Permalink to this definition">¶</a></dt>
<dd><p>Return x minus the mean(x).</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>x</strong> <span class="classifier-delimiter">:</span> <span class="classifier">array or sequence</span></dt>
<dd><p class="first last">Array or sequence containing the data
Can have any dimensionality</p>
</dd>
<dt><strong>axis</strong> <span class="classifier-delimiter">:</span> <span class="classifier">integer</span></dt>
<dd><p class="first last">The axis along which to take the mean. See numpy.mean for a
description of this argument.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_linear" title="matplotlib.mlab.detrend_linear"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_linear</span></code></a></dt>
<dd>Another detrend algorithm.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_none" title="matplotlib.mlab.detrend_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_none</span></code></a></dt>
<dd>Another detrend algorithm.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend" title="matplotlib.mlab.detrend"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend</span></code></a></dt>
<dd>A wrapper around all the detrend algorithms.</dd>
</dl>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.detrend_none">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">detrend_none</code><span class="sig-paren">(</span><em>x</em>, <em>axis=None</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#detrend_none"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.detrend_none" title="Permalink to this definition">¶</a></dt>
<dd><p>Return x: no detrending.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>x</strong> <span class="classifier-delimiter">:</span> <span class="classifier">any object</span></dt>
<dd><p class="first last">An object containing the data</p>
</dd>
<dt><strong>axis</strong> <span class="classifier-delimiter">:</span> <span class="classifier">integer</span></dt>
<dd><p class="first last">This parameter is ignored.
It is included for compatibility with detrend_mean</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_mean" title="matplotlib.mlab.detrend_mean"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_mean</span></code></a></dt>
<dd>Another detrend algorithm.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_linear" title="matplotlib.mlab.detrend_linear"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend_linear</span></code></a></dt>
<dd>Another detrend algorithm.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend" title="matplotlib.mlab.detrend"><code class="xref py py-obj docutils literal notranslate"><span class="pre">detrend</span></code></a></dt>
<dd>A wrapper around all the detrend algorithms.</dd>
</dl>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.magnitude_spectrum">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">magnitude_spectrum</code><span class="sig-paren">(</span><em>x</em>, <em>Fs=None</em>, <em>window=None</em>, <em>pad_to=None</em>, <em>sides=None</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#magnitude_spectrum"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.magnitude_spectrum" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the magnitude (absolute value) of the frequency spectrum of
<em>x</em>. Data is padded to a length of <em>pad_to</em> and the windowing function
<em>window</em> is applied to the signal.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>x</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array or sequence</span></dt>
<dd><p class="first last">Array or sequence containing the data</p>
</dd>
<dt><strong>Fs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">scalar</span></dt>
<dd><p class="first last">The sampling frequency (samples per time unit). It is used
to calculate the Fourier frequencies, freqs, in cycles per time
unit. The default value is 2.</p>
</dd>
<dt><strong>window</strong> <span class="classifier-delimiter">:</span> <span class="classifier">callable or ndarray</span></dt>
<dd><p class="first last">A function or a vector of length <em>NFFT</em>. To create window vectors see
<a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_hanning</span></code></a>, <a class="reference internal" href="#matplotlib.mlab.window_none" title="matplotlib.mlab.window_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_none</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.blackman.html#numpy.blackman" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.blackman</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.hamming.html#numpy.hamming" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.hamming</span></code></a>,
<a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.bartlett.html#numpy.bartlett" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.bartlett</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/signal.html#module-scipy.signal" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.signal</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.get_window.html#scipy.signal.get_window" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.signal.get_window</span></code></a>, etc. The
default is <a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_hanning</span></code></a>. If a function is passed as the argument,
it must take a data segment as an argument and return the windowed
version of the segment.</p>
</dd>
<dt><strong>sides</strong> <span class="classifier-delimiter">:</span> <span class="classifier">{'default', 'onesided', 'twosided'}</span></dt>
<dd><p class="first last">Specifies which sides of the spectrum to return. Default gives the
default behavior, which returns one-sided for real data and both
for complex data. 'onesided' forces the return of a one-sided
spectrum, while 'twosided' forces two-sided.</p>
</dd>
<dt><strong>pad_to</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int</span></dt>
<dd><p class="first last">The number of points to which the data segment is padded when
performing the FFT. While not increasing the actual resolution of
the spectrum (the minimum distance between resolvable peaks),
this can give more points in the plot, allowing for more
detail. This corresponds to the <em>n</em> parameter in the call to fft().
The default is None, which sets <em>pad_to</em> equal to the length of the
input signal (i.e. no padding).</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>spectrum</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array</span></dt>
<dd><p class="first last">The values for the magnitude spectrum (real valued)</p>
</dd>
<dt><strong>freqs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array</span></dt>
<dd><p class="first last">The frequencies corresponding to the elements in <em>spectrum</em></p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.psd" title="matplotlib.mlab.psd"><code class="xref py py-obj docutils literal notranslate"><span class="pre">psd</span></code></a></dt>
<dd>Returns the power spectral density.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.complex_spectrum" title="matplotlib.mlab.complex_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">complex_spectrum</span></code></a></dt>
<dd>This function returns the absolute value of <a class="reference internal" href="#matplotlib.mlab.complex_spectrum" title="matplotlib.mlab.complex_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">complex_spectrum</span></code></a>.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.angle_spectrum" title="matplotlib.mlab.angle_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">angle_spectrum</span></code></a></dt>
<dd>Returns the angles of the corresponding frequencies.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.phase_spectrum" title="matplotlib.mlab.phase_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">phase_spectrum</span></code></a></dt>
<dd>Returns the phase (unwrapped angle) of the corresponding frequencies.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.specgram" title="matplotlib.mlab.specgram"><code class="xref py py-obj docutils literal notranslate"><span class="pre">specgram</span></code></a></dt>
<dd>Can return the complex spectrum of segments within the signal.</dd>
</dl>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.phase_spectrum">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">phase_spectrum</code><span class="sig-paren">(</span><em>x</em>, <em>Fs=None</em>, <em>window=None</em>, <em>pad_to=None</em>, <em>sides=None</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#phase_spectrum"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.phase_spectrum" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the phase of the frequency spectrum (unwrapped angle spectrum) of
<em>x</em>. Data is padded to a length of <em>pad_to</em> and the windowing function
<em>window</em> is applied to the signal.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>x</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array or sequence</span></dt>
<dd><p class="first last">Array or sequence containing the data</p>
</dd>
<dt><strong>Fs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">scalar</span></dt>
<dd><p class="first last">The sampling frequency (samples per time unit). It is used
to calculate the Fourier frequencies, freqs, in cycles per time
unit. The default value is 2.</p>
</dd>
<dt><strong>window</strong> <span class="classifier-delimiter">:</span> <span class="classifier">callable or ndarray</span></dt>
<dd><p class="first last">A function or a vector of length <em>NFFT</em>. To create window vectors see
<a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_hanning</span></code></a>, <a class="reference internal" href="#matplotlib.mlab.window_none" title="matplotlib.mlab.window_none"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_none</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.blackman.html#numpy.blackman" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.blackman</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.hamming.html#numpy.hamming" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.hamming</span></code></a>,
<a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.bartlett.html#numpy.bartlett" title="(in NumPy v1.17)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.bartlett</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/signal.html#module-scipy.signal" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.signal</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.get_window.html#scipy.signal.get_window" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.signal.get_window</span></code></a>, etc. The
default is <a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">window_hanning</span></code></a>. If a function is passed as the argument,
it must take a data segment as an argument and return the windowed
version of the segment.</p>
</dd>
<dt><strong>sides</strong> <span class="classifier-delimiter">:</span> <span class="classifier">{'default', 'onesided', 'twosided'}</span></dt>
<dd><p class="first last">Specifies which sides of the spectrum to return. Default gives the
default behavior, which returns one-sided for real data and both
for complex data. 'onesided' forces the return of a one-sided
spectrum, while 'twosided' forces two-sided.</p>
</dd>
<dt><strong>pad_to</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int</span></dt>
<dd><p class="first last">The number of points to which the data segment is padded when
performing the FFT. While not increasing the actual resolution of
the spectrum (the minimum distance between resolvable peaks),
this can give more points in the plot, allowing for more
detail. This corresponds to the <em>n</em> parameter in the call to fft().
The default is None, which sets <em>pad_to</em> equal to the length of the
input signal (i.e. no padding).</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>spectrum</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array</span></dt>
<dd><p class="first last">The values for the phase spectrum in radians (real valued)</p>
</dd>
<dt><strong>freqs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array</span></dt>
<dd><p class="first last">The frequencies corresponding to the elements in <em>spectrum</em></p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.complex_spectrum" title="matplotlib.mlab.complex_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">complex_spectrum</span></code></a></dt>
<dd>This function returns the phase value of <a class="reference internal" href="#matplotlib.mlab.complex_spectrum" title="matplotlib.mlab.complex_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">complex_spectrum</span></code></a>.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.magnitude_spectrum" title="matplotlib.mlab.magnitude_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">magnitude_spectrum</span></code></a></dt>
<dd>Returns the magnitudes of the corresponding frequencies.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.angle_spectrum" title="matplotlib.mlab.angle_spectrum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">angle_spectrum</span></code></a></dt>
<dd>Returns the angle (wrapped phase) of the corresponding frequencies.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.specgram" title="matplotlib.mlab.specgram"><code class="xref py py-obj docutils literal notranslate"><span class="pre">specgram</span></code></a></dt>
<dd>Can return the complex spectrum of segments within the signal.</dd>
</dl>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.psd">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">psd</code><span class="sig-paren">(</span><em>x</em>, <em>NFFT=None</em>, <em>Fs=None</em>, <em>detrend=None</em>, <em>window=None</em>, <em>noverlap=None</em>, <em>pad_to=None</em>, <em>sides=None</em>, <em>scale_by_freq=None</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/matplotlib/mlab.html#psd"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#matplotlib.mlab.psd" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the power spectral density.</p>
<p>The power spectral density <span class="math notranslate nohighlight">\(P_{xx}\)</span> by Welch's average
periodogram method. The vector <em>x</em> is divided into <em>NFFT</em> length
segments. Each segment is detrended by function <em>detrend</em> and
windowed by function <em>window</em>. <em>noverlap</em> gives the length of
the overlap between segments. The <span class="math notranslate nohighlight">\(|\mathrm{fft}(i)|^2\)</span>
of each segment <span class="math notranslate nohighlight">\(i\)</span> are averaged to compute <span class="math notranslate nohighlight">\(P_{xx}\)</span>.</p>
<p>If len(<em>x</em>) < <em>NFFT</em>, it will be zero padded to <em>NFFT</em>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">