scipy.signal.csd¶

scipy.signal.
csd
(x, y, fs=1.0, window='hann', nperseg=None, noverlap=None, nfft=None, detrend='constant', return_onesided=True, scaling='density', axis=1, average='mean')[source]¶ Estimate the cross power spectral density, Pxy, using Welch’s method.
Parameters:  x : array_like
Time series of measurement values
 y : array_like
Time series of measurement values
 fs : float, optional
Sampling frequency of the x and y time series. Defaults to 1.0.
 window : str or tuple or array_like, optional
Desired window to use. If window is a string or tuple, it is passed to
get_window
to generate the window values, which are DFTeven by default. Seeget_window
for a list of windows and required parameters. If window is array_like it will be used directly as the window and its length must be nperseg. Defaults to a Hann window. nperseg : int, optional
Length of each segment. Defaults to None, but if window is str or tuple, is set to 256, and if window is array_like, is set to the length of the window.
 noverlap: int, optional
Number of points to overlap between segments. If None,
noverlap = nperseg // 2
. Defaults to None. nfft : int, optional
Length of the FFT used, if a zero padded FFT is desired. If None, the FFT length is nperseg. Defaults to None.
 detrend : str or function or False, optional
Specifies how to detrend each segment. If
detrend
is a string, it is passed as the type argument to thedetrend
function. If it is a function, it takes a segment and returns a detrended segment. Ifdetrend
is False, no detrending is done. Defaults to ‘constant’. return_onesided : bool, optional
If True, return a onesided spectrum for real data. If False return a twosided spectrum. Defaults to True, but for complex data, a twosided spectrum is always returned.
 scaling : { ‘density’, ‘spectrum’ }, optional
Selects between computing the cross spectral density (‘density’) where Pxy has units of V**2/Hz and computing the cross spectrum (‘spectrum’) where Pxy has units of V**2, if x and y are measured in V and fs is measured in Hz. Defaults to ‘density’
 axis : int, optional
Axis along which the CSD is computed for both inputs; the default is over the last axis (i.e.
axis=1
). average : { ‘mean’, ‘median’ }, optional
Method to use when averaging periodograms. Defaults to ‘mean’.
New in version 1.2.0.
Returns:  f : ndarray
Array of sample frequencies.
 Pxy : ndarray
Cross spectral density or cross power spectrum of x,y.
See also
periodogram
 Simple, optionally modified periodogram
lombscargle
 LombScargle periodogram for unevenly sampled data
welch
 Power spectral density by Welch’s method. [Equivalent to csd(x,x)]
coherence
 Magnitude squared coherence by Welch’s method.
Notes
By convention, Pxy is computed with the conjugate FFT of X multiplied by the FFT of Y.
If the input series differ in length, the shorter series will be zeropadded to match.
An appropriate amount of overlap will depend on the choice of window and on your requirements. For the default Hann window an overlap of 50% is a reasonable trade off between accurately estimating the signal power, while not over counting any of the data. Narrower windows may require a larger overlap.
New in version 0.16.0.
References
[1] P. Welch, “The use of the fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms”, IEEE Trans. Audio Electroacoust. vol. 15, pp. 7073, 1967. [2] Rabiner, Lawrence R., and B. Gold. “Theory and Application of Digital Signal Processing” PrenticeHall, pp. 414419, 1975 Examples
>>> from scipy import signal >>> import matplotlib.pyplot as plt
Generate two test signals with some common features.
>>> fs = 10e3 >>> N = 1e5 >>> amp = 20 >>> freq = 1234.0 >>> noise_power = 0.001 * fs / 2 >>> time = np.arange(N) / fs >>> b, a = signal.butter(2, 0.25, 'low') >>> x = np.random.normal(scale=np.sqrt(noise_power), size=time.shape) >>> y = signal.lfilter(b, a, x) >>> x += amp*np.sin(2*np.pi*freq*time) >>> y += np.random.normal(scale=0.1*np.sqrt(noise_power), size=time.shape)
Compute and plot the magnitude of the cross spectral density.
>>> f, Pxy = signal.csd(x, y, fs, nperseg=1024) >>> plt.semilogy(f, np.abs(Pxy)) >>> plt.xlabel('frequency [Hz]') >>> plt.ylabel('CSD [V**2/Hz]') >>> plt.show()