Fast Fourier Transform

An implementation of a Fast Fourier Transform, Inverse Fast Fourier Transform, and a frequency calculator for the FFT.

This library is part of audiergon, built by Hamd Waseem (https://github.com/hamdivazim/Audiergon)

Available Methods:

iterative_fft
iterative_ifft
iterative_fftfreq

Dependencies:

cmath
audiergon.bit_reverse

audiergon.fast_fourier_transform.iterative_fft(arr)[source]

An iterative Fast Fourier Transform implementation within Python.

Computes the one-dimensional discrete Fourier Transform (DFT) of an array using the Cooley-Tukey algorithm.

Parameters:: arr (list or numpy.ndarray) – The time-domain samples to be transformed.
Returns:: A list of complex numbers representing the frequency spectrum.
Return type:: list
Raises:: ValueError – If the length of the array is not a power of two.

audiergon.fast_fourier_transform.iterative_fftfreq(l, d=1.0)[source]

An iterative calculation of the frequencies for the FFT output.

Generates the sample frequencies for each bin location based on the total sequence window length and spacing interval.

Parameters:

l (int) – Window length (number of bins).
d (float, optional) – Sample spacing/interval (inverse of the sampling rate), defaults to 1.0.

Returns:

A list containing the calculated frequency values for each bin.

Return type:

list

Raises:

ValueError – If the length of the frame is not a power of two.

audiergon.fast_fourier_transform.iterative_ifft(arr)[source]

An iterative Inverse Fast Fourier Transform implementation within Python.

Computes the inverse discrete Fourier Transform (DFT) to convert a frequency-domain array back into the time-domain, utilising the Cooley-Tukey algorithm.

Parameters:: arr (list or numpy.ndarray) – The complex frequency-domain coefficients.
Returns:: An array of numbers scaled down by the sequence length.
Return type:: numpy.ndarray
Raises:: ValueError – If the length of the array is not a power of two.