fftfreq

The function fftfreq is a numerical routine provided by the NumPy library in Python. It generates an array of sample frequencies for use with real and complex discrete Fourier transforms performed by the numpy.fft module. The name stands for frequency domain for Fourier Transform. The function requires the length of the signal, N, and optionally the sample spacing, d, which defaults to one. The output is a one‑dimensional array of length N containing frequency bins that correspond to the order of components returned by the Discrete Fourier Transform.

The computed frequencies are in units of the inverse of d. For even N, the array contains values from 0 up to 1/(2d) – the Nyquist frequency – followed by negative frequencies below zero. For odd N, the positive range extends to (N‑1)/2, and the negative frequencies follow. This ordering matches the result of the numpy.fft.fft routine. The function may also take a second argument, dtype, to specify the desired output data type.

A typical usage example is to plot the magnitude spectrum of an audio signal sampled at 44100 Hz and to determine the frequency of a periodic component. By passing N and d to fftfreq, one obtains the proper frequency axis for the array returned by fft. The function is also used in correlation and convolution analysis, where the frequency domain is needed for efficient computation.

Related functions include fftshift, ifftshift, rfftfreq, and irfftfreq, which are designed for handling shifted frequency arrays and real‑valued transforms. Standard documentation for NumPy provides full parameter listings, examples, and references to the mathematical basis of the discrete Fourier transform.