ESP32 FFT

This provides a vanilla radix-2 FFT out-of-place implementation and a test example.

Author

This code was written by Robin Scheibler during rainy days in October 2017.

Example

#include "fft.h"

...

// Create the FFT config structure
fft_config_t *real_fft_plan = fft_init(NFFT, FFT_REAL, FFT_FORWARD, NULL, NULL);

// Fill array with some data
for (k = 0 ; k < fft_analysis->size ; k++)
  real_fft_plan->input[k] = (float)k;

// Execute transformation
fft_execute(real_fft_plan);

// Now do something with the output
printf("DC component : %f\n", real_fft_plan->output[0]);  // DC is at [0]
for (k = 1 ; k < real_fft_plan->size / 2 ; k++)
  printf("%d-th freq : %f+j%f\n", k, real_fft_plan->output[2*k], real_fft_plan->output[2*k+1]);
printf("Middle component : %f\n", real_fft_plan->output[1]);  // N/2 is real and stored at [1]

// Don't forget to clean up at the end to free all the memory that was allocated
fft_destroy(real_fft_plan)

Documentation

1. Create the FFT configuration by running fft_init.

    fft_config_t *fft_init(int size, fft_type_t type, fft_direction_t direction, float *input, float *output)
   
    Parameters
    ----------
    size : int
        The FFT size (should be a power of two), if not, returns NULL.
    type : fft_type_t
        The type of FFT, FFT_REAL or FFT_COMPLEX
    direction : fft_direction_t
        The direction, FFT_FORWARD or FFT_BACKWARD (inverse transformation)
    input : float *
        A pointer to a buffer of the correct size. If NULL, a buffer is allocated dynamically
    output : float *
        A pointer to a buffer of the correct size. If NULL, a buffer is allocated dynamically.
   
    Returns
    -------
    A pointer to an `fft_config_t` structure that holds pointers to the buffers and
    all the necessary configuration options.
   

2. Fill data in the input buffer

3. Call fft_execute to run the FFT

4. Use the transformed data located in the output buffer

5. Possibly free up memory by calling fft_destroy on the configuration structure

Note about Inverse Real FFT

When doing an inverse real FFT, the data in the input buffer is destroyed.

Buffer sizes and data organization

• For FFT_REAL FFTs (forward as well as backward) of size NFFT, the buffer is of size NFFT. Then, the input data is organized as

    Input  : [ x[0], x[1], x[2], ..., x[NFFT-1] ]
    Output : [ X[0], X[NFFT/2], Re(X[1]), Im(X[1]), ..., Re(X[NFFT/2-1]), Im(X[NFFT/2-1]) ]
  

• For FFT_COMPLEX of size NFFT, the buffer is of size 2 * NFFT as both real and imaginary parts should be saved.

    Input  : [ Re(x[0]), Im(x[0]), ..., Re(x[NFFT-1]), Im(x[NFFT-1]) ]
    Output : [ Re(X[0]), Im(X[0]), ..., Re(X[NFFT-1]), Im(X[NFFT-1]) ]
  

License

This software is released under the MIT license.

Copyright (c) 2017 Robin Scheibler

Permission is hereby granted, free of charge, to any person obtaining a copy
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furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
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