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# numpy.fft.fftfreq

fft.fftfreq(n, d=1.0, 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.

    device str, optional

      The device on which to place the created array. Default: `None`. For Array-API interoperability only, so must be `"cpu"` if passed.

      New in version 2.0.0.

  Returns:
    f ndarray

      Array of length n containing the sample frequencies.

  Examples

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