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<!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 3.2.0 documentation</title>

title="Search within Matplotlib 3.2.0 documentation"

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

</head><body>

<div id="unreleased-message"> You are reading an old version of the documentation (v3.2.0). For the latest version see <a href="/stable/">https://matplotlib.org/stable/</a> </div>

<div style="float: left; position: absolute; width: 496px; bottom: 0; padding-bottom: 24px">Version 3.2.0</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>

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</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.

"""

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

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

sides=None):

"""

Compute the angle of the frequency spectrum (wrapped phase spectrum) of

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

*window* is applied to the signal.

Parameters

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