matplotlib.mlab
¶
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 complexvalued 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 memoryefficient manner
stride_repeat
 Repeat an array in a memoryefficient manner
apply_window
 Apply a window along a given axis

class
matplotlib.mlab.
GaussianKDE
(dataset, bw_method=None)[source]¶ Bases:
object
Representation of a kerneldensity estimate using Gaussian kernels.
Parameters:  datasetarraylike
Datapoints to estimate from. In case of univariate data this is a 1D array, otherwise a 2D array with shape (# of dims, # of data).
 bw_methodstr, scalar or callable, optional
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
kde.factor
. If a callable, it should take aGaussianKDE
instance as only parameter and return a scalar. If None (default), 'scott' is used.
Attributes:  datasetndarray
The dataset with which
gaussian_kde
was initialized. dimint
Number of dimensions.
 num_dpint
Number of datapoints.
 factorfloat
The bandwidth factor, obtained from
kde.covariance_factor
, with which the covariance matrix is multiplied. covariancendarray
The covariance matrix of dataset, scaled by the calculated bandwidth (
kde.factor
). inv_covndarray
The inverse of covariance.
Methods
kde.evaluate(points) (ndarray) Evaluate the estimated pdf on a provided set of points. kde(points) (ndarray) Same as kde.evaluate(points) 
covariance_factor
(self)¶

evaluate
(self, points)[source]¶ Evaluate the estimated pdf on a set of points.
Parameters:  points(# of dimensions, # of points)array
Alternatively, a (# of dimensions,) vector can be passed in and treated as a single point.
Returns:  values(# of points,)array
The values at each point.
Raises:  ValueErrorif the dimensionality of the input points is different
than the dimensionality of the KDE.

matplotlib.mlab.
angle_spectrum
(x, Fs=None, window=None, pad_to=None, sides=None)[source]¶ 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:  x1D array or sequence
Array or sequence containing the data
 Fsscalar
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.
 windowcallable 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 iswindow_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 onesided for real data and both for complex data. 'onesided' forces the return of a onesided spectrum, while 'twosided' forces twosided.
 pad_toint
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).
Returns:  spectrum1D array
The values for the angle spectrum in radians (real valued)
 freqs1D array
The frequencies corresponding to the elements in spectrum
See also
complex_spectrum
 This function returns the angle value of
complex_spectrum
. magnitude_spectrum
 Returns the magnitudes 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.

matplotlib.mlab.
apply_window
(x, window, axis=0, return_window=None)[source]¶ [Deprecated] Apply the given window to the given 1D or 2D array along the given axis.
Parameters:  x1D or 2D array or sequence
Array or sequence containing the data.
 windowfunction or array.
Either a function to generate a window or an array with length x.shape[axis]
 axisinteger
The axis over which to do the repetition. Must be 0 or 1. The default is 0
 return_windowbool
If true, also return the 1D values of the window that was applied
Notes
Deprecated since version 3.2.

matplotlib.mlab.
cohere
(x, y, NFFT=256, Fs=2, detrend=<function detrend_none at 0x7f65b0d01290>, window=<function window_hanning at 0x7f65ac56ee60>, noverlap=0, pad_to=None, sides='default', scale_by_freq=None)[source]¶ The coherence between x and y. Coherence is the normalized cross spectral density:
\[C_{xy} = \frac{P_{xy}^2}{P_{xx}P_{yy}}\]Parameters:  x, y
Array or sequence containing the data
 Fsscalar
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.
 windowcallable 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 iswindow_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 onesided for real data and both for complex data. 'onesided' forces the return of a onesided spectrum, while 'twosided' forces twosided.
 pad_toint
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
 NFFTint
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 ffting, 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
mlab
module definesdetrend_none
,detrend_mean
, anddetrend_linear
, but you can use a custom function as well. You can also use a string to choose one of the functions: 'none' callsdetrend_none
. 'mean' callsdetrend_mean
. 'linear' callsdetrend_linear
. scale_by_freqbool, 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.
 noverlapinteger
The number of points of overlap between blocks. The default value is 0 (no overlap).
Returns:  The return value is the tuple (Cxy, f), where f are the
 frequencies of the coherence vector. For cohere, scaling the
 individual densities by the sampling frequency has no effect,
 since the factors cancel out.

matplotlib.mlab.
complex_spectrum
(x, Fs=None, window=None, pad_to=None, sides=None)[source]¶ Compute the complexvalued frequency spectrum of x. Data is padded to a length of pad_to and the windowing function window is applied to the signal.
Parameters:  x1D array or sequence
Array or sequence containing the data
 Fsscalar
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.
 windowcallable 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 iswindow_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 onesided for real data and both for complex data. 'onesided' forces the return of a onesided spectrum, while 'twosided' forces twosided.
 pad_toint
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).
Returns:  spectrum1D array
The values for the complex spectrum (complex valued)
 freqs1D 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.

matplotlib.mlab.
csd
(x, y, NFFT=None, Fs=None, detrend=None, window=None, noverlap=None, pad_to=None, sides=None, scale_by_freq=None)[source]¶ Compute the crossspectral density.
The cross spectral density \(P_{xy}\) 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 \(P_{xy}\), 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, y1D arrays or sequences
Arrays or sequences containing the data
 Fsscalar
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.
 windowcallable 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 iswindow_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 onesided for real data and both for complex data. 'onesided' forces the return of a onesided spectrum, while 'twosided' forces twosided.
 pad_toint
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
 NFFTint
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 ffting, 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
mlab
module definesdetrend_none
,detrend_mean
, anddetrend_linear
, but you can use a custom function as well. You can also use a string to choose one of the functions: 'none' callsdetrend_none
. 'mean' callsdetrend_mean
. 'linear' callsdetrend_linear
. scale_by_freqbool, 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.
 noverlapinteger
The number of points of overlap between segments. The default value is 0 (no overlap).
Returns:  Pxy1D array
The values for the cross spectrum
P_{xy}
before scaling (real valued) freqs1D array
The frequencies corresponding to the elements in Pxy
See also
psd
 equivalent to setting
y = x
.
References
Bendat & Piersol  Random Data: Analysis and Measurement Procedures, John Wiley & Sons (1986)

matplotlib.mlab.
demean
(x, axis=0)[source]¶ [Deprecated] Return x minus its mean along the specified axis.
Parameters:  xarray or sequence
Array or sequence containing the data Can have any dimensionality
 axisinteger
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.
Notes
Deprecated since version 3.1.

matplotlib.mlab.
detrend
(x, key=None, axis=None)[source]¶ Return x with its trend removed.
Parameters:  xarray 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 asdetrend_linear
. 'none' is the same asdetrend_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. axisinteger
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.

matplotlib.mlab.
detrend_linear
(y)[source]¶ Return x minus best fit line; 'linear' detrending.
Parameters:  y0D or 1D array or sequence
Array or sequence containing the data
 axisinteger
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.

matplotlib.mlab.
detrend_mean
(x, axis=None)[source]¶ Return x minus the mean(x).
Parameters:  xarray or sequence
Array or sequence containing the data Can have any dimensionality
 axisinteger
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.

matplotlib.mlab.
detrend_none
(x, axis=None)[source]¶ Return x: no detrending.
Parameters:  xany object
An object containing the data
 axisinteger
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.

matplotlib.mlab.
magnitude_spectrum
(x, Fs=None, window=None, pad_to=None, sides=None)[source]¶ 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:  x1D array or sequence
Array or sequence containing the data
 Fsscalar
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.
 windowcallable 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 iswindow_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 onesided for real data and both for complex data. 'onesided' forces the return of a onesided spectrum, while 'twosided' forces twosided.
 pad_toint
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).
Returns:  spectrum1D array
The values for the magnitude spectrum (real valued)
 freqs1D 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.

matplotlib.mlab.
phase_spectrum
(x, Fs=None, window=None, pad_to=None, sides=None)[source]¶ Compute the phase of the frequency spectrum (unwrapped angle spectrum) of x. Data is padded to a length of pad_to and the windowing function window is applied to the signal.
Parameters:  x1D array or sequence
Array or sequence containing the data
 Fsscalar
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.
 windowcallable 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 iswindow_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 onesided for real data and both for complex data. 'onesided' forces the return of a onesided spectrum, while 'twosided' forces twosided.
 pad_toint
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).
Returns:  spectrum1D array
The values for the phase spectrum in radians (real valued)
 freqs1D array
The frequencies corresponding to the elements in spectrum
See also
complex_spectrum
 This function returns the phase value of
complex_spectrum
. magnitude_spectrum
 Returns the magnitudes of the corresponding frequencies.
angle_spectrum
 Returns the angle (wrapped phase) of the corresponding frequencies.
specgram
 Can return the complex spectrum of segments within the signal.

matplotlib.mlab.
psd
(x, NFFT=None, Fs=None, detrend=None, window=None, noverlap=None, pad_to=None, sides=None, scale_by_freq=None)[source]¶ Compute the power spectral density.
The power spectral density \(P_{xx}\) 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 \(\mathrm{fft}(i)^2\) of each segment \(i\) are averaged to compute \(P_{xx}\).
If len(x) < NFFT, it will be zero padded to NFFT.
Parameters:  x1D array or sequence
Array or sequence containing the data
 Fsscalar
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.
 windowcallable 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 iswindow_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 onesided for real data and both for complex data. 'onesided' forces the return of a onesided spectrum, while 'twosided' forces twosided.
 pad_toint
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
 NFFTint
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 ffting, 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
mlab
module definesdetrend_none
,detrend_mean
, anddetrend_linear
, but you can use a custom function as well. You can also use a string to choose one of the functions: 'none' callsdetrend_none
. 'mean' callsdetrend_mean
. 'linear' callsdetrend_linear
. scale_by_freqbool, 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.
 noverlapinteger
The number of points of overlap between segments. The default value is 0 (no overlap).
Returns:  Pxx1D array
The values for the power spectrum
P_{xx}
(real valued) freqs1D array
The frequencies corresponding to the elements in Pxx
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.
References
Bendat & Piersol  Random Data: Analysis and Measurement Procedures, John Wiley & Sons (1986)

matplotlib.mlab.
specgram
(x, NFFT=None, Fs=None, detrend=None, window=None, noverlap=None, pad_to=None, sides=None, scale_by_freq=None, mode=None)[source]¶ Compute a spectrogram.
Compute and plot a spectrogram of data in x. Data are split into NFFT length segments and the spectrum of each section is computed. The windowing function window is applied to each segment, and the amount of overlap of each segment is specified with noverlap.
Parameters:  xarraylike
1D array or sequence.
 Fsscalar
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.
 windowcallable 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 iswindow_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 onesided for real data and both for complex data. 'onesided' forces the return of a onesided spectrum, while 'twosided' forces twosided.
 pad_toint
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
 NFFTint
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 ffting, 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
mlab
module definesdetrend_none
,detrend_mean
, anddetrend_linear
, but you can use a custom function as well. You can also use a string to choose one of the functions: 'none' callsdetrend_none
. 'mean' callsdetrend_mean
. 'linear' callsdetrend_linear
. scale_by_freqbool, 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.
 noverlapint, optional
The number of points of overlap between blocks. The default value is 128.
 modestr, optional
 What sort of spectrum to use, default is 'psd'.
 'psd'
Returns the power spectral density.
 'complex'
Returns the complexvalued frequency spectrum.
 'magnitude'
Returns the magnitude spectrum.
 'angle'
Returns the phase spectrum without unwrapping.
 'phase'
Returns the phase spectrum with unwrapping.
Returns:  spectrumarraylike
2D array, columns are the periodograms of successive segments.
 freqsarraylike
1D array, frequencies corresponding to the rows in spectrum.
 tarraylike
1D array, the times corresponding to midpoints of segments (i.e the columns in spectrum).
See also
psd
 differs in the overlap and in the return values.
complex_spectrum
 similar, but with complex valued frequencies.
magnitude_spectrum
 similar single segment when mode is 'magnitude'.
angle_spectrum
 similar to single segment when mode is 'angle'.
phase_spectrum
 similar to single segment when mode is 'phase'.
Notes
detrend and scale_by_freq only apply when mode is set to 'psd'.

matplotlib.mlab.
stride_repeat
(x, n, axis=0)[source]¶ [Deprecated] Repeat the values in an array in a memoryefficient 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:  x1D array or sequence
Array or sequence containing the data.
 ninteger
The number of time to repeat the array.
 axisinteger
The axis along which the data will run.
Notes
Deprecated since version 3.2.
References

matplotlib.mlab.
stride_windows
(x, n, noverlap=None, axis=0)[source]¶ 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:  x1D array or sequence
Array or sequence containing the data.
 ninteger
The number of data points in each window.
 noverlapinteger
The overlap between adjacent windows. Default is 0 (no overlap)
 axisinteger
The axis along which the windows will run.
References
stackoverflow: Rolling window for 1D arrays in Numpy? stackoverflow: Using strides for an efficient moving average filter

matplotlib.mlab.
window_hanning
(x)[source]¶ Return x times the hanning window of len(x).
See also
window_none
 Another window algorithm.

matplotlib.mlab.
window_none
(x)[source]¶ No window function; simply return x.
See also
window_hanning
 Another window algorithm.