rfft.h

Public domain single header fast Fourier transform for arbitrary array sizes,
in about 100 lines of C code, which should be straightforward to understand.
By Grego.

A C++ implementation using the stdlib complex and vector is also provided in rfft.hpp.

Installation

Run:

``sh
$ npm i rfft.c
`

And then include rfft.h or rfft.hpp as follows:

`cxx
// main.c or main.cxx
#define RFFT_IMPLEMENTATION
#include // if using C, or
#include // if using C++

int main() { / ... / }
`

Finally, compile while adding the path node_modules/rfft.c to your compiler's include paths.

`bash
$ gcc -I./node_modules/rfft.c main.c # if using C, or
$ g++ -I./node_modules/rfft.c main.cxx # if using C++
`

You may also use a simpler approach with the cpoach tool, which automatically adds the necessary include paths of all the installed dependencies for your project.

`bash
$ cpoach gcc main.c # if using C, or
$ cpoach g++ main.cxx # if using C++
`

Algorithms

The classic Cooley-Turkey algorithm
is used in place (without additional allocations) for arrays of size 2^k.

For more more general ones, Bluestein algorithm
is used. It utilizes the binomial identity 2nk = n^2 + k^2 - (k - n)^2 to
express the Fourier transform as a convolution of two sequences,
which can be computed using the algorith for the power of 2 sizes.
It needs to allocate two auxillary array of size at most 4n + 3.

The runnig time is always O(n log(n))`. However, if the speed is crucial,
more optimized libraries like FFTW are recommended.

Inspiration

Inspired by Project Nayuki,
but written in a simpler and arguably more straightforward way.

License

Public domain.