cupyx.scipy.signal.welch(x, fs=1.0, window='hann', nperseg=None, noverlap=None, nfft=None, detrend='constant', return_onesided=True, scaling='density', axis=-1, average='mean')[source]#

Estimate power spectral density using Welch’s method.

Welch’s method [1] computes an estimate of the power spectral density by dividing the data into overlapping segments, computing a modified periodogram for each segment and averaging the periodograms.

  • x (array_like) – Time series of measurement values

  • fs (float, optional) – Sampling frequency of the x 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 power spectral density (‘density’) where Pxx has units of V**2/Hz and computing the power spectrum (‘spectrum’) where Pxx has units of V**2, if x is measured in V and fs is measured in Hz. Defaults to ‘density’

  • axis (int, optional) – Axis along which the periodogram is computed; the default is over the last axis (i.e. axis=-1).

  • average ({ 'mean', 'median' }, optional) – Method to use when averaging periodograms. Defaults to ‘mean’.


  • f (ndarray) – Array of sample frequencies.

  • Pxx (ndarray) – Power spectral density or power spectrum of x.

See also


Simple, optionally modified periodogram


Lomb-Scargle periodogram for unevenly sampled data


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.

If noverlap is 0, this method is equivalent to Bartlett’s method [2].