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| 1 | +/* Factored discrete Fourier transform, or FFT, and its inverse iFFT */ |
| 2 | + |
| 3 | +#include <assert.h> |
| 4 | +#include <math.h> |
| 5 | +#include <stdio.h> |
| 6 | +#include <stdlib.h> |
| 7 | + |
| 8 | +#define q 15 /* for 2^3 points */ |
| 9 | +#define N (1<<q) /* N-point FFT, iFFT */ |
| 10 | + |
| 11 | +typedef float real; |
| 12 | +typedef struct{real Re; real Im;} complex; |
| 13 | + |
| 14 | +#ifndef PI |
| 15 | +# define PI 3.14159265358979323846264338327950288 |
| 16 | +#endif |
| 17 | + |
| 18 | + |
| 19 | +/* Print a vector of complexes as ordered pairs. */ |
| 20 | +static void print_vector( const char *title, complex *x, int n) { |
| 21 | + |
| 22 | + int i; |
| 23 | + |
| 24 | + printf("%s (dim=%d):", title, n); |
| 25 | + |
| 26 | + for(i=0; i<(n<8?n:8); i++ ) { |
| 27 | + printf(" %5.2f,%5.2f ", x[i].Re,x[i].Im); |
| 28 | + } |
| 29 | + |
| 30 | + putchar('\n'); |
| 31 | + |
| 32 | + return; |
| 33 | +} |
| 34 | + |
| 35 | +/* |
| 36 | + fft(v,N): |
| 37 | + [0] If N==1 then return. |
| 38 | + [1] For k = 0 to N/2-1, let ve[k] = v[2*k] |
| 39 | + [2] Compute fft(ve, N/2); |
| 40 | + [3] For k = 0 to N/2-1, let vo[k] = v[2*k+1] |
| 41 | + [4] Compute fft(vo, N/2); |
| 42 | + [5] For m = 0 to N/2-1, do [6] through [9] |
| 43 | + [6] Let w.re = cos(2*PI*m/N) |
| 44 | + [7] Let w.im = -sin(2*PI*m/N) |
| 45 | + [8] Let v[m] = ve[m] + w*vo[m] |
| 46 | + [9] Let v[m+N/2] = ve[m] - w*vo[m] |
| 47 | + */ |
| 48 | +void fft( complex *v, int n, complex *tmp ) { |
| 49 | + |
| 50 | + if(n>1) { /* otherwise, do nothing and return */ |
| 51 | + int k,m; complex z, w, *vo, *ve; |
| 52 | + ve = tmp; vo = tmp+n/2; |
| 53 | + for(k=0; k<n/2; k++) { |
| 54 | + ve[k] = v[2*k]; |
| 55 | + vo[k] = v[2*k+1]; |
| 56 | + } |
| 57 | + fft( ve, n/2, v ); /* FFT on even-indexed elements of v[] */ |
| 58 | + fft( vo, n/2, v ); /* FFT on odd-indexed elements of v[] */ |
| 59 | + for(m=0; m<n/2; m++) { |
| 60 | + w.Re = cos(2*PI*m/(double)n); |
| 61 | + w.Im = -sin(2*PI*m/(double)n); |
| 62 | + z.Re = w.Re*vo[m].Re - w.Im*vo[m].Im; /* Re(w*vo[m]) */ |
| 63 | + z.Im = w.Re*vo[m].Im + w.Im*vo[m].Re; /* Im(w*vo[m]) */ |
| 64 | + v[ m ].Re = ve[m].Re + z.Re; |
| 65 | + v[ m ].Im = ve[m].Im + z.Im; |
| 66 | + v[m+n/2].Re = ve[m].Re - z.Re; |
| 67 | + v[m+n/2].Im = ve[m].Im - z.Im; |
| 68 | + } |
| 69 | + } |
| 70 | + return; |
| 71 | +} |
| 72 | + |
| 73 | +/* |
| 74 | + ifft(v,N): |
| 75 | + [0] If N==1 then return. |
| 76 | + [1] For k = 0 to N/2-1, let ve[k] = v[2*k] |
| 77 | + [2] Compute ifft(ve, N/2); |
| 78 | + [3] For k = 0 to N/2-1, let vo[k] = v[2*k+1] |
| 79 | + [4] Compute ifft(vo, N/2); |
| 80 | + [5] For m = 0 to N/2-1, do [6] through [9] |
| 81 | + [6] Let w.re = cos(2*PI*m/N) |
| 82 | + [7] Let w.im = sin(2*PI*m/N) |
| 83 | + [8] Let v[m] = ve[m] + w*vo[m] |
| 84 | + [9] Let v[m+N/2] = ve[m] - w*vo[m] |
| 85 | + */ |
| 86 | +void ifft( complex *v, int n, complex *tmp ) { |
| 87 | + |
| 88 | + if(n>1) { /* otherwise, do nothing and return */ |
| 89 | + int k,m; complex z, w, *vo, *ve; |
| 90 | + ve = tmp; vo = tmp+n/2; |
| 91 | + for(k=0; k<n/2; k++) { |
| 92 | + ve[k] = v[2*k]; |
| 93 | + vo[k] = v[2*k+1]; |
| 94 | + } |
| 95 | + ifft( ve, n/2, v ); /* FFT on even-indexed elements of v[] */ |
| 96 | + ifft( vo, n/2, v ); /* FFT on odd-indexed elements of v[] */ |
| 97 | + for(m=0; m<n/2; m++) { |
| 98 | + w.Re = cos(2*PI*m/(double)n); |
| 99 | + w.Im = sin(2*PI*m/(double)n); |
| 100 | + z.Re = w.Re*vo[m].Re - w.Im*vo[m].Im; /* Re(w*vo[m]) */ |
| 101 | + z.Im = w.Re*vo[m].Im + w.Im*vo[m].Re; /* Im(w*vo[m]) */ |
| 102 | + v[ m ].Re = ve[m].Re + z.Re; |
| 103 | + v[ m ].Im = ve[m].Im + z.Im; |
| 104 | + v[m+n/2].Re = ve[m].Re - z.Re; |
| 105 | + v[m+n/2].Im = ve[m].Im - z.Im; |
| 106 | + } |
| 107 | + } |
| 108 | + return; |
| 109 | +} |
| 110 | + |
| 111 | +int main(void) { |
| 112 | + |
| 113 | + complex v[N], v1[N], scratch[N]; |
| 114 | + int k; |
| 115 | + |
| 116 | + for (int x=0; x<10000; x++) { |
| 117 | + /* Fill v[] with a function of known FFT: */ |
| 118 | + for(k=0; k<N; k++) { |
| 119 | + v[k].Re = 0.125 * cos(2*PI*k/(double)N); |
| 120 | + v[k].Im = 0.125 * sin(2*PI*k/(double)N); |
| 121 | + v1[k].Re = 0.3 * cos(2*PI*k/(double)N); |
| 122 | + v1[k].Im = -0.3 * sin(2*PI*k/(double)N); |
| 123 | + } |
| 124 | + |
| 125 | + /* FFT, iFFT of v[]: */ |
| 126 | + print_vector("Orig", v, N); |
| 127 | + fft( v, N, scratch ); |
| 128 | + print_vector(" FFT", v, N); |
| 129 | + ifft( v, N, scratch ); |
| 130 | + print_vector("iFFT", v, N); |
| 131 | + |
| 132 | + /* FFT, iFFT of v1[]: */ |
| 133 | + print_vector("Orig", v1, N); |
| 134 | + fft( v1, N, scratch ); |
| 135 | + print_vector(" FFT", v1, N); |
| 136 | + ifft( v1, N, scratch ); |
| 137 | + print_vector("iFFT", v1, N); |
| 138 | + } |
| 139 | + |
| 140 | + exit(EXIT_SUCCESS); |
| 141 | +} |
| 142 | + |
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