# 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')

  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 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’.

    return_onesided bool, optional

      If True, return a one-sided spectrum for real data. If False return a two-sided spectrum. Defaults to 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 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. If the spectrum is complex, the average is computed separately for the real and imaginary parts. 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`

    Lomb-Scargle 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 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.

  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. 70-73, 1967.

  [2]

  Rabiner, Lawrence R., and B. Gold. “Theory and Application of Digital Signal Processing” Prentice-Hall, pp. 414-419, 1975

  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 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()