Fast Fourier Transformation

This is my Radix-2 FFT library, which was first developped for an embedded system consisting of a Texas Instrument ARM Cortex-M0 with a 128x96 OLED display. Since then, I've used it on in a homebrew for the PSVita made by Sony. You can find the source for the homebrew in my repositories.

It is based on the schematic representation of a Radix-2 FFT:

*source for image : https://hkn.illinois.edu/wiki/wiki:signal_processing:fft

Dependencies:

• Only std includes used

The library should be cross-platform compatible.

How to change number of FFT points

There are 3 defines that control the FFT. These have a default value you can see below.

If you want to change this, you'll have to define them in your Makefile or CMakeLists. With cmake, add the defines like so : "add_definitions(-DFFT_POINT=1024)"

/* DEFAULT VALUES */#ifndefFFT_POINT/* N */#defineFFT_POINT 512
#endif#ifndefFFT_POINT_2/* N/2 */#defineFFT_POINT_2 256
#endif#ifndefFFT_STAGES/* log(N)/log(2) */#defineFFT_STAGES 9
#endif

For a 1024 point FFT you have to set the defines to 1024, 512, 10, respectively.

Note: The library (and Radix-2 fft) has been made in such a way that the FFT point value is expected to be a value of 2^X. If you try a different value, it is highly likely that it will not work as intended and crash or not work at all.

Library functions:

The functions are divided in two groups:

• Functions to execute before the main FFT loop and only once:

voidfft_BlockPerStage(uint16_t*pblocks);
voidfft_ButterfliesPerBlocks(uint16_t*pbutterflies);
voidfft_BitReversedLUT(uint16_t*pbit_reversed);
voidfft_TwiddleFactor(Complex*pW);
voidfft_Window(uint8_ttype, float*pWin);

• Functions to execute continuously before and after each FFT computation:

voidfft_DataToComplex(float*px, float*pWin, Complex*pdata_complex, uint16_t*pbit_reversed);
voidfft_Compute(Complex*pdata_complex, Complex*pW, uint16_t*pblocks, uint16_t*pbutterflies);
voidfft_ComplexToMagnPhase(Complex*pdata_complex, FFT*pspectrum, uint8_tnormalize);
ORvoidfft_ComplexTodB(Complex*pdata_complex, FFT*pspectrum);	

How to calculate the phase:

For this you'll have to uncomment a define in fft.h.

/************** * Uncomment to calculate phase * #define FFT_PHASE_USE **************/

Window function for the FFT

The library has 7 different windows that you can use on your samples:

/* Types of window */#defineFFT_WIN_RECTANGLE 0
#defineFFT_WIN_TRIANGLE 1
#defineFFT_WIN_HANNING 2
#defineFFT_WIN_HAMMING 3
#defineFFT_WIN_BLACKMAN 4
#defineFFT_WIN_NUTTALL 5
#defineFFT_WIN_FLAT_TOP 6

Use this with the fft_Window() function.

This is to be used before your main loop, to initialize a float window array.

If you don't know what this is go to this wikipedia page for more info.

License

Creative Commons Attribution-ShareAlike 4.0 International, see LICENSE.md.