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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')

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 zero-padded 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.

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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 :None:None:`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 :None:None:`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:None:`None`, noverlap = nperseg // 2 . Defaults to :None:None:`None`.

nfft : int, optional

Length of the FFT used, if a zero padded FFT is desired. If :None:None:`None`, the FFT length is :None:None:`nperseg`. Defaults to :None:None:`None`.

detrend : str or function or `False`, optional

Specifies how to detrend each segment. If detrend is a string, it is passed as the :None:None:`type` argument to the detrend function. If it is a function, it takes a segment and returns a detrended segment. If detrend is :None:None:`False`, no detrending is done. Defaults to 'constant'.

return_onesided : bool, optional

If :None:None:`True`, return a one-sided spectrum for real data. If :None:None:`False` return a two-sided spectrum. Defaults to :None:None:`True`, but for complex data, a two-sided spectrum is always returned.

scaling : { 'density', 'spectrum' }, optional

Selects between computing the cross spectral density ('density') where :None:None:`Pxy` has units of V**2/Hz and computing the cross spectrum ('spectrum') where :None:None:`Pxy` has units of V**2, if x and y are measured in V and :None:None:`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. If the spectrum is complex, the average is computed separately for the real and imaginary parts. Defaults to 'mean'.

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Returns

f : ndarray

Array of sample frequencies.

Pxy : ndarray

Cross spectral density or cross power spectrum of x,y.

Estimate the cross power spectral density, Pxy, using Welch's method.

See Also

coherence

Magnitude squared coherence by Welch's method.

lombscargle

Lomb-Scargle periodogram for unevenly sampled data

periodogram

Simple, optionally modified periodogram

welch

Power spectral density by Welch's method. [Equivalent to csd(x,x)]

Examples

>>> 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 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()
See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.signal._spectral_py.coherence scipy.signal._spectral_py.stft scipy.signal._spectral_py.csd scipy.signal._spectral_py.spectrogram scipy.signal._spectral_py.lombscargle

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GitHub : /scipy/signal/_spectral_py.py#454
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