r2cfft - a small wrapper to simplify FFT/IFFTs of real-valued sequences

[jasonconway]

I wanted to share a small wrapper function I wrote for the CMSIS arm_rfft_fast_f32() function. It is intended to provide a higher efficiency, near-drop-in-replacement for instances where arm_cfft_f32() is being used with real-valued sequences, and an algorithm based around using n+1 complex-conjugate-symmetric coefficients (as output by arm_rfft_fast_f32()) isn't available or unrealistic to implement.

A detailed description alongside some performance comparisons can be found on the project's GitHub page.

Its use cases are likely quite niche, but hopefully someone finds it useful!

[tschrama]

What is the advantage of arm_rfft_fast_f32() over arm_cfft_f32()?

[MarkT]

Uses half as much memory and nearly twice as fast I suspect. An N-point FFT with real inputs can be done using an N/2-point complex FFT
using some clever pre- and post-processing.

An N-point complex-in complex-out FFT needs 2N floats for the inputs and outputs
An N-point real-in complex-out FFT needs N floats for the inputs and outputs (since the negative frequency bins
are redundant, being complex conjugates of the positive frequency bins)