# scipy.fft.fftfreq#

scipy.fft.fftfreq(n, d=1.0, *, xp=None, device=None)[source]#

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:
nint

Window length.

dscalar, optional

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

xparray_namespace, optional

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

devicedevice, optional

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

Returns:
fndarray

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])
```