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Module « scipy.signal »

Fonction coherence - module scipy.signal

Signature de la fonction coherence

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

Description

help(scipy.signal.coherence)

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.

.. versionadded:: 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. 70-73, 1967.
.. [2] Stoica, Petre, and Randolph Moses, "Spectral Analysis of
       Signals" Prentice Hall, 2005

Examples
--------
>>> import numpy as np
>>> from scipy import signal
>>> import matplotlib.pyplot as plt
>>> rng = np.random.default_rng()

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 = rng.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 += rng.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')
>>> plt.show()

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