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# scipy.fft.fftfreq

scipy.fft.fftfreq(n, d=1.0, *, xp=None, device=None)

  Return the Discrete Fourier Transform sample frequencies.

  The returned float array f contains the frequency bin centers in cycles per unit of the sample spacing (with zero at the start). For instance, if the sample spacing is in seconds, then the frequency unit is cycles/second.

  Given a window length n and a sample spacing d:

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

  Parameters:
    n int

      Window length.

    d scalar, optional

      Sample spacing (inverse of the sampling rate). Defaults to 1.

    xp array_namespace, optional

      The namespace for the return array. Default is None, where NumPy is used.

    device device, optional

      The device for the return array. Only valid when xp.fft.fftfreq implements the device parameter.

  Returns:
    f ndarray

      Array of length n containing the sample frequencies.

  Examples

      >>> import numpy as np
      >>> import scipy.fft
      >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
      >>> fourier = scipy.fft.fft(signal)
      >>> n = signal.size
      >>> timestep = 0.1
      >>> freq = scipy.fft.fftfreq(n, d=timestep)
      >>> freq
      array([ 0.  ,  1.25,  2.5 , ..., -3.75, -2.5 , -1.25])