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120 lines
5.6 KiB
C
120 lines
5.6 KiB
C
/*
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* fft.h is Based on
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* Free FFT and convolution (C)
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*
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* Copyright (c) 2019 Project Nayuki. (MIT License)
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* https://www.nayuki.io/page/free-small-fft-in-multiple-languages
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy of
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* this software and associated documentation files (the "Software"), to deal in
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* the Software without restriction, including without limitation the rights to
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* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
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* the Software, and to permit persons to whom the Software is furnished to do so,
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* subject to the following conditions:
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* - The above copyright notice and this permission notice shall be included in
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* all copies or substantial portions of the Software.
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* - The Software is provided "as is", without warranty of any kind, express or
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* implied, including but not limited to the warranties of merchantability,
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* fitness for a particular purpose and noninfringement. In no event shall the
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* authors or copyright holders be liable for any claim, damages or other
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* liability, whether in an action of contract, tort or otherwise, arising from,
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* out of or in connection with the Software or the use or other dealings in the
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* Software.
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*/
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#include <math.h>
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#include <stdint.h>
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static uint16_t reverse_bits(uint16_t x, int n) {
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uint16_t result = 0;
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for (int i = 0; i < n; i++, x >>= 1)
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result = (result << 1) | (x & 1U);
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return result;
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}
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static const float sin_table[] = {
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/*
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* float has about 7.2 digits of precision
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for (uint8_t i = 0; i < FFT_SIZE - (FFT_SIZE / 4); i++) {
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printf("% .8f,%c", sin(2 * M_PI * i / FFT_SIZE), i % 8 == 7 ? '\n' : ' ');
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}
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*/
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0.00000000, 0.02454123, 0.04906767, 0.07356456, 0.09801714, 0.12241068, 0.14673047, 0.17096189,
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0.19509032, 0.21910124, 0.24298018, 0.26671276, 0.29028468, 0.31368174, 0.33688985, 0.35989504,
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0.38268343, 0.40524131, 0.42755509, 0.44961133, 0.47139674, 0.49289819, 0.51410274, 0.53499762,
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0.55557023, 0.57580819, 0.59569930, 0.61523159, 0.63439328, 0.65317284, 0.67155895, 0.68954054,
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0.70710678, 0.72424708, 0.74095113, 0.75720885, 0.77301045, 0.78834643, 0.80320753, 0.81758481,
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0.83146961, 0.84485357, 0.85772861, 0.87008699, 0.88192126, 0.89322430, 0.90398929, 0.91420976,
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0.92387953, 0.93299280, 0.94154407, 0.94952818, 0.95694034, 0.96377607, 0.97003125, 0.97570213,
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0.98078528, 0.98527764, 0.98917651, 0.99247953, 0.99518473, 0.99729046, 0.99879546, 0.99969882,
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1.00000000, 0.99969882, 0.99879546, 0.99729046, 0.99518473, 0.99247953, 0.98917651, 0.98527764,
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0.98078528, 0.97570213, 0.97003125, 0.96377607, 0.95694034, 0.94952818, 0.94154407, 0.93299280,
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0.92387953, 0.91420976, 0.90398929, 0.89322430, 0.88192126, 0.87008699, 0.85772861, 0.84485357,
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0.83146961, 0.81758481, 0.80320753, 0.78834643, 0.77301045, 0.75720885, 0.74095113, 0.72424708,
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0.70710678, 0.68954054, 0.67155895, 0.65317284, 0.63439328, 0.61523159, 0.59569930, 0.57580819,
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0.55557023, 0.53499762, 0.51410274, 0.49289819, 0.47139674, 0.44961133, 0.42755509, 0.40524131,
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0.38268343, 0.35989504, 0.33688985, 0.31368174, 0.29028468, 0.26671276, 0.24298018, 0.21910124,
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0.19509032, 0.17096189, 0.14673047, 0.12241068, 0.09801714, 0.07356456, 0.04906767, 0.02454123,
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0.00000000, -0.02454123, -0.04906767, -0.07356456, -0.09801714, -0.12241068, -0.14673047, -0.17096189,
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-0.19509032, -0.21910124, -0.24298018, -0.26671276, -0.29028468, -0.31368174, -0.33688985, -0.35989504,
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-0.38268343, -0.40524131, -0.42755509, -0.44961133, -0.47139674, -0.49289819, -0.51410274, -0.53499762,
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-0.55557023, -0.57580819, -0.59569930, -0.61523159, -0.63439328, -0.65317284, -0.67155895, -0.68954054,
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-0.70710678, -0.72424708, -0.74095113, -0.75720885, -0.77301045, -0.78834643, -0.80320753, -0.81758481,
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-0.83146961, -0.84485357, -0.85772861, -0.87008699, -0.88192126, -0.89322430, -0.90398929, -0.91420976,
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-0.92387953, -0.93299280, -0.94154407, -0.94952818, -0.95694034, -0.96377607, -0.97003125, -0.97570213,
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-0.98078528, -0.98527764, -0.98917651, -0.99247953, -0.99518473, -0.99729046, -0.99879546, -0.99969882,
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};
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/***
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* dir = forward: 0, inverse: 1
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* https://www.nayuki.io/res/free-small-fft-in-multiple-languages/fft.c
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*/
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static void fft256(float array[][2], const uint8_t dir) {
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const uint16_t n = 256;
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const uint8_t levels = 8; // log2(n)
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const float* const cos_table = &sin_table[64];
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const uint8_t real = dir & 1;
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const uint8_t imag = ~real & 1;
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for (uint16_t i = 0; i < n; i++) {
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uint16_t j = reverse_bits(i, levels);
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if (j > i) {
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float temp = array[i][real];
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array[i][real] = array[j][real];
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array[j][real] = temp;
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temp = array[i][imag];
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array[i][imag] = array[j][imag];
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array[j][imag] = temp;
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}
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}
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// Cooley-Tukey decimation-in-time radix-2 FFT
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for (uint16_t size = 2; size <= n; size *= 2) {
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uint16_t halfsize = size / 2;
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uint16_t tablestep = n / size;
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for (uint16_t i = 0; i < n; i += size) {
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for (uint16_t j = i, k = 0; j < i + halfsize; j++, k += tablestep) {
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uint16_t l = j + halfsize;
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float tpre = array[l][real] * cos_table[k] + array[l][imag] * sin_table[k];
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float tpim = -array[l][real] * sin_table[k] + array[l][imag] * cos_table[k] ;
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array[l][real] = array[j][real] - tpre;
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array[l][imag] = array[j][imag] - tpim;
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array[j][real] += tpre;
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array[j][imag] += tpim;
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}
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}
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if (size == n) // Prevent overflow in 'size *= 2'
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break;
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}
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}
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static inline void fft256_forward(float array[][2]) {
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fft256(array, 0);
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}
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static inline void fft256_inverse(float array[][2]) {
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fft256(array, 1);
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}
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