scipy.signal.coherence(x, y, fs=1.0, window='hann', nperseg=None, noverlap=None, nfft=None, detrend='constant', axis=-1)[source]

Estimate the magnitude squared coherence estimate, Cxy, of discrete-time signals X and Y using Welch’s method.

Cxy = abs(Pxy)**2/(Pxx*Pyy), where Pxx and Pyy are power spectral density estimates of X and Y, and Pxy is the cross spectral density estimate of X and Y.


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 DFT-even by default. See get_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 the detrend function. If it is a function, it takes a segment and returns a detrended segment. If detrend is False, no detrending is done. Defaults to ‘constant’.

axis : int, optional

Axis along which the coherence is computed for both inputs; the default is over the last axis (i.e. axis=-1).


f : ndarray

Array of sample frequencies.

Cxy : ndarray

Magnitude squared coherence of x and y.

See also

Simple, optionally modified periodogram
Lomb-Scargle periodogram for unevenly sampled data
Power spectral density by Welch’s method.
Cross spectral density by Welch’s method.


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.


[R244]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. 70-73, 1967.
[R245]Stoica, Petre, and Randolph Moses, “Spectral Analysis of Signals” Prentice Hall, 2005


>>> 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 coherence.

>>> f, Cxy = signal.coherence(x, y, fs, nperseg=1024)
>>> plt.semilogy(f, Cxy)
>>> plt.xlabel('frequency [Hz]')
>>> plt.ylabel('Coherence')

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