matplotlib.github.com/3.2.1/_modules/matplotlib/mlab.html at main · matplotlib/matplotlib.github.com

History

1674 lines (1333 loc) · 173 KB

Raw

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">

<head>

<title>matplotlib.mlab — Matplotlib 3.2.1 documentation</title>

title="Search within Matplotlib 3.2.1 documentation"

href="../../_static/opensearch.xml"/>

</head><body>

<div id="unreleased-message"> You are reading an old version of the documentation (v3.2.1). For the latest version see <a href="/stable/">https://matplotlib.org/stable/</a> </div>

John Hunter Excellence in Plotting Contest 2020

<a href="https://jhepc.github.io/about.html"> submissions are open!

</a>

Entries are due June 1, 2020.

</div>

<div style="float: left; position: absolute; width: 496px; bottom: 0; padding-bottom: 24px">Version 3.2.1</div>

<div id="forkongithub"><a href="https://github.com/matplotlib/matplotlib">Fork me on GitHub</a></div>

</div>

<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>

</form>

</li>

</ul>

</nav>

<h3>Navigation</h3>

<ul>

<a href="../../genindex.html" title="General Index"

accesskey="I">index</a></li>

<a href="../../py-modindex.html" title="Python Module Index"

>modules</a> |</li>

<li><a href="../../contents.html">contents</a> »</li>

<li class="nav-item nav-item-1"><a href="../index.html" >Module code</a> »</li>

<li class="nav-item nav-item-2"><a href="../matplotlib.html" accesskey="U">matplotlib</a> »</li>

</ul>

</div>

<h3>Related Topics</h3>

<ul>

<li><a href="../../contents.html">Documentation overview</a><ul>

<li><a href="../index.html">Module code</a><ul>

<li><a href="../matplotlib.html">matplotlib</a><ul>

</ul></li>

</ul>

</div>

<h1>Source code for matplotlib.mlab</h1><div class="highlight"><pre>

"""

Numerical python functions written for compatibility with MATLAB

commands with the same names. Most numerical python functions can be found in

the `numpy` and `scipy` libraries. What remains here is code for performing

spectral computations.

Spectral functions

-------------------

`cohere`

Coherence (normalized cross spectral density)

`csd`

Cross spectral density using Welch's average periodogram

`detrend`

Remove the mean or best fit line from an array

`psd`

Power spectral density using Welch's average periodogram

`specgram`

Spectrogram (spectrum over segments of time)

`complex_spectrum`

Return the complex-valued frequency spectrum of a signal

`magnitude_spectrum`

Return the magnitude of the frequency spectrum of a signal

`angle_spectrum`

Return the angle (wrapped phase) of the frequency spectrum of a signal

`phase_spectrum`

Return the phase (unwrapped angle) of the frequency spectrum of a signal

`detrend_mean`

Remove the mean from a line.

`detrend_linear`

Remove the best fit line from a line.

`detrend_none`

Return the original line.

`stride_windows`

Get all windows in an array in a memory-efficient manner

`stride_repeat`

Repeat an array in a memory-efficient manner

`apply_window`

Apply a window along a given axis

"""

import csv

import inspect

from numbers import Number

import numpy as np

import matplotlib.cbook as cbook

from matplotlib import docstring

<div class="viewcode-block" id="window_hanning"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.window_hanning">[docs]</a>def window_hanning(x):

'''

Return x times the hanning window of len(x).

See Also

--------

window_none : Another window algorithm.

'''

return np.hanning(len(x))*x</div>

<div class="viewcode-block" id="window_none"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.window_none">[docs]</a>def window_none(x):

'''

No window function; simply return x.

See Also

--------

window_hanning : Another window algorithm.

'''

return x</div>

<div class="viewcode-block" id="apply_window"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.apply_window">[docs]</a>@cbook.deprecated("3.2")

def apply_window(x, window, axis=0, return_window=None):

'''

Apply the given window to the given 1D or 2D array along the given axis.

Parameters

----------

x : 1D or 2D array or sequence

Array or sequence containing the data.

window : function or array.

Either a function to generate a window or an array with length

*x*.shape[*axis*]

axis : integer

The axis over which to do the repetition.

Must be 0 or 1. The default is 0

return_window : bool

If true, also return the 1D values of the window that was applied

'''

x = np.asarray(x)

if x.ndim < 1 or x.ndim > 2:

raise ValueError('only 1D or 2D arrays can be used')

if axis+1 > x.ndim:

raise ValueError('axis(=%s) out of bounds' % axis)

xshape = list(x.shape)

xshapetarg = xshape.pop(axis)

if np.iterable(window):

if len(window) != xshapetarg:

raise ValueError('The len(window) must be the same as the shape '

'of x for the chosen axis')

windowVals = window

else:

windowVals = window(np.ones(xshapetarg, dtype=x.dtype))

if x.ndim == 1:

if return_window:

return windowVals * x, windowVals

else:

return windowVals * x

xshapeother = xshape.pop()

otheraxis = (axis+1) % 2

windowValsRep = stride_repeat(windowVals, xshapeother, axis=otheraxis)

if return_window:

return windowValsRep * x, windowVals

else:

return windowValsRep * x</div>

<div class="viewcode-block" id="detrend"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.detrend">[docs]</a>def detrend(x, key=None, axis=None):

'''

Return x with its trend removed.

Parameters

----------

x : array or sequence

Array or sequence containing the data.

key : {'default', 'constant', 'mean', 'linear', 'none'} or function

Specifies the detrend algorithm to use. 'default' is 'mean', which is

the same as `detrend_mean`. 'constant' is the same. 'linear' is

the same as `detrend_linear`. 'none' is the same as

`detrend_none`. 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.

axis : integer

The axis along which to do the detrending.

See Also

--------

detrend_mean : Implementation of the 'mean' algorithm.

detrend_linear : Implementation of the 'linear' algorithm.

detrend_none : Implementation of the 'none' algorithm.

'''

if key is None or key in ['constant', 'mean', 'default']:

return detrend(x, key=detrend_mean, axis=axis)

elif key == 'linear':

return detrend(x, key=detrend_linear, axis=axis)

elif key == 'none':

return detrend(x, key=detrend_none, axis=axis)

elif callable(key):

if axis is not None and axis + 1 > x.ndim:

raise ValueError(f'axis(={axis}) out of bounds')

if (axis is None and x.ndim == 0) or (not axis and x.ndim == 1):

return key(x)

# try to use the 'axis' argument if the function supports it,

# otherwise use apply_along_axis to do it

try:

return key(x, axis=axis)

except TypeError:

return np.apply_along_axis(key, axis=axis, arr=x)

else:

raise ValueError(

f"Unknown value for key: {key!r}, must be one of: 'default', "

f"'constant', 'mean', 'linear', or a function")</div>

<div class="viewcode-block" id="demean"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.demean">[docs]</a>@cbook.deprecated("3.1", alternative="detrend_mean")

def demean(x, axis=0):

'''

Return x minus its mean along the specified axis.

Parameters

----------

x : array or sequence

Array or sequence containing the data

Can have any dimensionality

axis : integer

The axis along which to take the mean. See numpy.mean for a

description of this argument.

See Also

--------

detrend_mean : Same as `demean` except for the default *axis*.

'''

return detrend_mean(x, axis=axis)</div>

<div class="viewcode-block" id="detrend_mean"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.detrend_mean">[docs]</a>def detrend_mean(x, axis=None):

'''

Return x minus the mean(x).

Parameters

----------

x : array or sequence

Array or sequence containing the data

Can have any dimensionality

axis : integer

The axis along which to take the mean. See numpy.mean for a

description of this argument.

See Also

--------

detrend_linear : Another detrend algorithm.

detrend_none : Another detrend algorithm.

detrend : A wrapper around all the detrend algorithms.

'''

if axis is not None and axis+1 > x.ndim:

return x - x.mean(axis, keepdims=True)</div>

<div class="viewcode-block" id="detrend_none"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.detrend_none">[docs]</a>def detrend_none(x, axis=None):

'''

Return x: no detrending.

Parameters

----------

x : any object

An object containing the data

axis : integer

This parameter is ignored.

It is included for compatibility with detrend_mean

See Also

--------

detrend_mean : Another detrend algorithm.

detrend_linear : Another detrend algorithm.

detrend : A wrapper around all the detrend algorithms.

'''

return x</div>

<div class="viewcode-block" id="detrend_linear"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.detrend_linear">[docs]</a>def detrend_linear(y):

'''

Return x minus best fit line; 'linear' detrending.

Parameters

----------

y : 0-D or 1-D array or sequence

Array or sequence containing the data

axis : integer

The axis along which to take the mean. See numpy.mean for a

description of this argument.

See Also

--------

detrend_mean : Another detrend algorithm.

detrend_none : Another detrend algorithm.

detrend : A wrapper around all the detrend algorithms.

'''

# This is faster than an algorithm based on linalg.lstsq.

y = np.asarray(y)

if y.ndim > 1:

raise ValueError('y cannot have ndim > 1')

# short-circuit 0-D array.

if not y.ndim:

return np.array(0., dtype=y.dtype)

x = np.arange(y.size, dtype=float)

C = np.cov(x, y, bias=1)

b = C[0, 1]/C[0, 0]

a = y.mean() - b*x.mean()

return y - (b*x + a)</div>

<div class="viewcode-block" id="stride_windows"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.stride_windows">[docs]</a>def stride_windows(x, n, noverlap=None, axis=0):

'''

Get all windows of x with length n as a single array,

using strides to avoid data duplication.

.. warning::

It is not safe to write to the output array. Multiple

elements may point to the same piece of memory,

so modifying one value may change others.

Parameters

----------

x : 1D array or sequence

Array or sequence containing the data.

n : integer

The number of data points in each window.

noverlap : integer

The overlap between adjacent windows.

Default is 0 (no overlap)

axis : integer

The axis along which the windows will run.

References

----------

`stackoverflow: Rolling window for 1D arrays in Numpy?

<http://stackoverflow.com/a/6811241>`_

`stackoverflow: Using strides for an efficient moving average filter

<http://stackoverflow.com/a/4947453>`_

'''

if noverlap is None:

noverlap = 0

if noverlap >= n:

raise ValueError('noverlap must be less than n')

if n < 1:

raise ValueError('n cannot be less than 1')

if x.ndim != 1:

raise ValueError('only 1-dimensional arrays can be used')

if n == 1 and noverlap == 0:

if axis == 0:

return x[np.newaxis]

else:

return x[np.newaxis].transpose()

if n > x.size:

raise ValueError('n cannot be greater than the length of x')

# np.lib.stride_tricks.as_strided easily leads to memory corruption for

# non integer shape and strides, i.e. noverlap or n. See #3845.

noverlap = int(noverlap)

n = int(n)

step = n - noverlap

if axis == 0:

shape = (n, (x.shape[-1]-noverlap)//step)

strides = (x.strides[0], step*x.strides[0])

else:

shape = ((x.shape[-1]-noverlap)//step, n)

strides = (step*x.strides[0], x.strides[0])

return np.lib.stride_tricks.as_strided(x, shape=shape, strides=strides)</div>

<div class="viewcode-block" id="stride_repeat"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.stride_repeat">[docs]</a>@cbook.deprecated("3.2")

def stride_repeat(x, n, axis=0):

'''

Repeat the values in an array in a memory-efficient manner. Array x is

stacked vertically n times.

.. warning::

It is not safe to write to the output array. Multiple

elements may point to the same piece of memory, so

modifying one value may change others.

Parameters

----------

x : 1D array or sequence

Array or sequence containing the data.

n : integer

The number of time to repeat the array.

axis : integer

The axis along which the data will run.

References

----------

`stackoverflow: Repeat NumPy array without replicating data?

<http://stackoverflow.com/a/5568169>`_

'''

if axis not in [0, 1]:

raise ValueError('axis must be 0 or 1')

if x.ndim != 1:

raise ValueError('only 1-dimensional arrays can be used')

if n == 1:

if axis == 0:

return np.atleast_2d(x)

else:

return np.atleast_2d(x).T

if n < 1:

raise ValueError('n cannot be less than 1')

# np.lib.stride_tricks.as_strided easily leads to memory corruption for

# non integer shape and strides, i.e. n. See #3845.

n = int(n)

if axis == 0:

shape = (n, x.size)

strides = (0, x.strides[0])

else:

shape = (x.size, n)

def _spectral_helper(x, y=None, NFFT=None, Fs=None, detrend_func=None,

window=None, noverlap=None, pad_to=None,

sides=None, scale_by_freq=None, mode=None):

'''

This is a helper function that implements the commonality between the

psd, csd, spectrogram and complex, magnitude, angle, and phase spectrums.

It is *NOT* meant to be used outside of mlab and may change at any time.

'''

if y is None:

# if y is None use x for y

same_data = True

else:

# The checks for if y is x are so that we can use the same function to

# implement the core of psd(), csd(), and spectrogram() without doing

# extra calculations. We return the unaveraged Pxy, freqs, and t.

same_data = y is x

if Fs is None:

Fs = 2

if noverlap is None:

noverlap = 0

if detrend_func is None:

detrend_func = detrend_none

if window is None:

window = window_hanning

# if NFFT is set to None use the whole signal

if NFFT is None:

NFFT = 256

if mode is None or mode == 'default':

mode = 'psd'

cbook._check_in_list(

['default', 'psd', 'complex', 'magnitude', 'angle', 'phase'],

mode=mode)

if not same_data and mode != 'psd':

raise ValueError("x and y must be equal if mode is not 'psd'")

# Make sure we're dealing with a numpy array. If y and x were the same

# object to start with, keep them that way

if not same_data:

if sides is None or sides == 'default':

if np.iscomplexobj(x):

sides = 'twosided'

else:

sides = 'onesided'

cbook._check_in_list(['default', 'onesided', 'twosided'], sides=sides)

# zero pad x and y up to NFFT if they are shorter than NFFT

if len(x) < NFFT:

n = len(x)

x = np.resize(x, NFFT)

x[n:] = 0

if not same_data and len(y) < NFFT:

n = len(y)

y = np.resize(y, NFFT)

y[n:] = 0

if pad_to is None:

pad_to = NFFT

if mode != 'psd':

scale_by_freq = False

elif scale_by_freq is None:

scale_by_freq = True

# For real x, ignore the negative frequencies unless told otherwise

if sides == 'twosided':

numFreqs = pad_to

if pad_to % 2:

freqcenter = (pad_to - 1)//2 + 1

else:

freqcenter = pad_to//2

scaling_factor = 1.

elif sides == 'onesided':

if pad_to % 2:

numFreqs = (pad_to + 1)//2

else:

numFreqs = pad_to//2 + 1

scaling_factor = 2.

if not np.iterable(window):

window = window(np.ones(NFFT, x.dtype))

raise ValueError(

"The window length must match the data's first dimension")

result = stride_windows(x, NFFT, noverlap, axis=0)

result = detrend(result, detrend_func, axis=0)

result = result * window.reshape((-1, 1))

result = np.fft.fft(result, n=pad_to, axis=0)[:numFreqs, :]

freqs = np.fft.fftfreq(pad_to, 1/Fs)[:numFreqs]

if not same_data:

# if same_data is False, mode must be 'psd'

resultY = stride_windows(y, NFFT, noverlap)

resultY = detrend(resultY, detrend_func, axis=0)

resultY = resultY * window.reshape((-1, 1))

resultY = np.fft.fft(resultY, n=pad_to, axis=0)[:numFreqs, :]

result = np.conj(result) * resultY

elif mode == 'psd':

elif mode == 'magnitude':

result = np.abs(result) / np.abs(window).sum()

elif mode == 'angle' or mode == 'phase':

# we unwrap the phase later to handle the onesided vs. twosided case

result = np.angle(result)

elif mode == 'complex':

result /= np.abs(window).sum()

if mode == 'psd':

# Also include scaling factors for one-sided densities and dividing by

# the sampling frequency, if desired. Scale everything, except the DC

# component and the NFFT/2 component:

# if we have a even number of frequencies, don't scale NFFT/2

if not NFFT % 2:

slc = slice(1, -1, None)

# if we have an odd number, just don't scale DC

else:

slc = slice(1, None, None)

result[slc] *= scaling_factor

# MATLAB divides by the sampling frequency so that density function

# has units of dB/Hz and can be integrated by the plotted frequency

# values. Perform the same scaling here.

if scale_by_freq:

result /= Fs

# Scale the spectrum by the norm of the window to compensate for

# windowing loss; see Bendat & Piersol Sec 11.5.2.

result /= (np.abs(window)**2).sum()

else:

# In this case, preserve power in the segment, not amplitude

t = np.arange(NFFT/2, len(x) - NFFT/2 + 1, NFFT - noverlap)/Fs

if sides == 'twosided':

# center the frequency range at zero

freqs = np.concatenate((freqs[freqcenter:], freqs[:freqcenter]))

result = np.concatenate((result[freqcenter:, :],

result[:freqcenter, :]), 0)

elif not pad_to % 2:

# get the last value correctly, it is negative otherwise

freqs[-1] *= -1

# we unwrap the phase here to handle the onesided vs. twosided case

if mode == 'phase':

result = np.unwrap(result, axis=0)

return result, freqs, t

def _single_spectrum_helper(x, mode, Fs=None, window=None, pad_to=None,

sides=None):

'''

This is a helper function that implements the commonality between the

complex, magnitude, angle, and phase spectrums.

It is *NOT* meant to be used outside of mlab and may change at any time.

'''

cbook._check_in_list(['complex', 'magnitude', 'angle', 'phase'], mode=mode)

if pad_to is None:

pad_to = len(x)

spec, freqs, _ = _spectral_helper(x=x, y=None, NFFT=len(x), Fs=Fs,

detrend_func=detrend_none, window=window,

noverlap=0, pad_to=pad_to,

sides=sides,

scale_by_freq=False,

mode=mode)

if mode != 'complex':

spec = spec.real

if spec.ndim == 2 and spec.shape[1] == 1:

spec = spec[:, 0]

return spec, freqs

# Split out these keyword docs so that they can be used elsewhere

docstring.interpd.update(Spectral=inspect.cleandoc("""

Fs : scalar

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.

window : callable or ndarray

A function or a vector of length *NFFT*. To create window vectors see

`window_hanning`, `window_none`, `numpy.blackman`, `numpy.hamming`,

`numpy.bartlett`, `scipy.signal`, `scipy.signal.get_window`, etc. The

default is `window_hanning`. 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.

sides : {'default', 'onesided', 'twosided'}

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.

"""))

docstring.interpd.update(Single_Spectrum=inspect.cleandoc("""

pad_to : int

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 *n* parameter in the call to fft().

The default is None, which sets *pad_to* equal to the length of the

input signal (i.e. no padding).

"""))

docstring.interpd.update(PSD=inspect.cleandoc("""

pad_to : int

The number of points to which the data segment is padded when

performing the FFT. This can be different from *NFFT*, 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 *n* parameter

in the call to fft(). The default is None, which sets *pad_to*

equal to *NFFT*

NFFT : int

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 *NOT* be used to get zero padding, or the scaling of the

result will be incorrect. Use *pad_to* for this instead.

detrend : {'none', 'mean', 'linear'} or callable, default 'none'

The function applied to each segment before fft-ing, designed to

remove the mean or linear trend. Unlike in MATLAB, where the

*detrend* parameter is a vector, in Matplotlib is it a function.

The :mod:`~matplotlib.mlab` module defines `.detrend_none`,

`.detrend_mean`, and `.detrend_linear`, but you can use a custom

function as well. You can also use a string to choose one of the

functions: 'none' calls `.detrend_none`. 'mean' calls `.detrend_mean`.

'linear' calls `.detrend_linear`.

scale_by_freq : bool, optional

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.

"""))

<div class="viewcode-block" id="psd"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.psd">[docs]</a>@docstring.dedent_interpd

def psd(x, NFFT=None, Fs=None, detrend=None, window=None,

noverlap=None, pad_to=None, sides=None, scale_by_freq=None):

r"""

Compute the power spectral density.

The power spectral density :math:`P_{xx}` by Welch's average

periodogram method. The vector *x* is divided into *NFFT* length

segments. Each segment is detrended by function *detrend* and

windowed by function *window*. *noverlap* gives the length of

the overlap between segments. The :math:`|\mathrm{fft}(i)|^2`

of each segment :math:`i` are averaged to compute :math:`P_{xx}`.

If len(*x*) < *NFFT*, it will be zero padded to *NFFT*.

Parameters

----------

x : 1-D array or sequence

Array or sequence containing the data

%(Spectral)s

%(PSD)s

noverlap : integer

The number of points of overlap between segments.

The default value is 0 (no overlap).

Returns

-------

Pxx : 1-D array

The values for the power spectrum `P_{xx}` (real valued)

freqs : 1-D array

The frequencies corresponding to the elements in *Pxx*

References

----------

Bendat & Piersol -- Random Data: Analysis and Measurement Procedures, John

Wiley & Sons (1986)

See Also

--------

specgram

`specgram` differs in the default overlap; in not returning the mean of

the segment periodograms; and in returning the times of the segments.

magnitude_spectrum : returns the magnitude spectrum.

csd : returns the spectral density between two signals.

"""

Pxx, freqs = csd(x=x, y=None, NFFT=NFFT, Fs=Fs, detrend=detrend,

window=window, noverlap=noverlap, pad_to=pad_to,

sides=sides, scale_by_freq=scale_by_freq)

return Pxx.real, freqs</div>

<div class="viewcode-block" id="csd"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.csd">[docs]</a>@docstring.dedent_interpd

def csd(x, y, NFFT=None, Fs=None, detrend=None, window=None,

"""

Compute the cross-spectral density.

The cross spectral density :math:`P_{xy}` by Welch's average

periodogram method. The vectors *x* and *y* are divided into

*NFFT* length segments. Each segment is detrended by function

*detrend* and windowed by function *window*. *noverlap* gives

the length of the overlap between segments. The product of

the direct FFTs of *x* and *y* are averaged over each segment

to compute :math:`P_{xy}`, with a scaling to correct for power

loss due to windowing.

If len(*x*) < *NFFT* or len(*y*) < *NFFT*, they will be zero

padded to *NFFT*.

Parameters

----------

x, y : 1-D arrays or sequences

Arrays or sequences containing the data

%(Spectral)s

%(PSD)s

noverlap : integer

The number of points of overlap between segments.

The default value is 0 (no overlap).

Returns

-------

Pxy : 1-D array

The values for the cross spectrum `P_{xy}` before scaling (real valued)

freqs : 1-D array

The frequencies corresponding to the elements in *Pxy*

References

----------

Bendat & Piersol -- Random Data: Analysis and Measurement Procedures, John

Wiley & Sons (1986)

See Also

--------

psd : equivalent to setting ``y = x``.

"""

if NFFT is None:

NFFT = 256

Pxy, freqs, _ = _spectral_helper(x=x, y=y, NFFT=NFFT, Fs=Fs,

detrend_func=detrend, window=window,

noverlap=noverlap, pad_to=pad_to,

mode='psd')

if Pxy.ndim == 2:

if Pxy.shape[1] > 1:

Pxy = Pxy.mean(axis=1)

else:

Pxy = Pxy[:, 0]

return Pxy, freqs</div>

<div class="viewcode-block" id="complex_spectrum"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.complex_spectrum">[docs]</a>@docstring.dedent_interpd

def complex_spectrum(x, Fs=None, window=None, pad_to=None,

sides=None):

"""

Compute the complex-valued frequency spectrum of *x*. Data is padded to a

length of *pad_to* and the windowing function *window* is applied to the

signal.

Parameters

----------

x : 1-D array or sequence

Array or sequence containing the data

%(Spectral)s

%(Single_Spectrum)s

Returns

-------

spectrum : 1-D array

The values for the complex spectrum (complex valued)

freqs : 1-D array

The frequencies corresponding to the elements in *spectrum*

See Also

--------

magnitude_spectrum

Returns the absolute value of this function.

angle_spectrum

Returns the angle of this function.

phase_spectrum

Returns the phase (unwrapped angle) of this function.

specgram

Can return the complex spectrum of segments within the signal.

"""

return _single_spectrum_helper(x=x, Fs=Fs, window=window, pad_to=pad_to,

sides=sides, mode='complex')</div>

<div class="viewcode-block" id="magnitude_spectrum"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.magnitude_spectrum">[docs]</a>@docstring.dedent_interpd

def magnitude_spectrum(x, Fs=None, window=None, pad_to=None,

sides=None):

"""

Compute the magnitude (absolute value) of the frequency spectrum of

*x*. Data is padded to a length of *pad_to* and the windowing function

*window* is applied to the signal.

Parameters

----------

x : 1-D array or sequence

Array or sequence containing the data

%(Spectral)s

%(Single_Spectrum)s

Returns

-------

spectrum : 1-D array

The values for the magnitude spectrum (real valued)

freqs : 1-D array

The frequencies corresponding to the elements in *spectrum*

See Also

--------

psd

Returns the power spectral density.

complex_spectrum

This function returns the absolute value of `complex_spectrum`.

angle_spectrum

Returns the angles of the corresponding frequencies.

phase_spectrum

Returns the phase (unwrapped angle) of the corresponding frequencies.

specgram

Can return the complex spectrum of segments within the signal.

"""

View remainder of file in raw view

Provide feedback

Saved searches

Use saved searches to filter your results more quickly

FilesExpand file tree

mlab.html

Latest commit

History

mlab.html

File metadata and controls