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 cross-spectral 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, y1-D arrays or sequences


Arrays or sequences containing the data  
Fsfloat, default: 2


The sampling frequency (samples per time unit). It is used to calculate the Fourier frequencies, freqs, in cycles per time unit.  
windowcallable or ndarray, default: window_hanning


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. 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'}, optional


Which sides of the spectrum to return. 'default' is one-sided for real data and two-sided for complex data. 'onesided' forces the return of a one-sided spectrum, while 'twosided' forces two-sided.  
pad_toint, optional


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, default: 256


The number of data points used in each block for the FFT. A power 2 is most efficient. 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 it is a function. The 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_freqbool, default: True


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, default: 0 (no overlap)


The number of points of overlap between segments.    Returns 
 
Pxy1-D array


The values for the cross spectrum \(P_{xy}\) before scaling (real valued)  
freqs1-D 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)