cupyx.scipy.signal.coherence

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

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.

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 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).

Returns:

• f (ndarray) – Array of sample frequencies.

• Cxy (ndarray) – Magnitude squared coherence of x and y.

See also

periodogram

Simple, optionally modified periodogram

lombscargle

Lomb-Scargle periodogram for unevenly sampled data

welch

Power spectral density by Welch’s method.

csd

Cross spectral density by Welch’s method.

Notes

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. See [1] and [2] for more information.

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. 70-73, 1967.

[2]

Stoica, Petre, and Randolph Moses, “Spectral Analysis of Signals” Prentice Hall, 2005

Examples

>>> import cupy as cp
>>> from cupyx.scipy.signal import butter, lfilter, coherence
>>> 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 = cupy.arange(N) / fs
>>> b, a = butter(2, 0.25, 'low')
>>> x = cupy.random.normal(
...         scale=cupy.sqrt(noise_power), size=time.shape)
>>> y = lfilter(b, a, x)
>>> x += amp * cupy.sin(2*cupy.pi*freq*time)
>>> y += cupy.random.normal(
...         scale=0.1*cupy.sqrt(noise_power), size=time.shape)

Compute and plot the coherence.

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