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9f135d5 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 | // Haar wavelet transform for signal processing and compression
// Simple discrete wavelet transform implementation
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#define SIGNAL_SIZE 8192
#define NUM_TRANSFORMS 500
void haar_transform_1d(double *signal, int n) {
double *temp = (double*)malloc(n * sizeof(double));
while (n > 1) {
int half = n / 2;
// Compute averages and differences
for (int i = 0; i < half; i++) {
temp[i] = (signal[2*i] + signal[2*i + 1]) / 2.0;
temp[half + i] = (signal[2*i] - signal[2*i + 1]) / 2.0;
}
// Copy back
for (int i = 0; i < n; i++) {
signal[i] = temp[i];
}
n = half;
}
free(temp);
}
void inverse_haar_transform_1d(double *signal, int original_size) {
double *temp = (double*)malloc(original_size * sizeof(double));
int n = 1;
while (n < original_size) {
int half = n;
n *= 2;
// Reconstruct from averages and differences
for (int i = 0; i < half; i++) {
temp[2*i] = signal[i] + signal[half + i];
temp[2*i + 1] = signal[i] - signal[half + i];
}
// Copy back
for (int i = 0; i < n; i++) {
signal[i] = temp[i];
}
}
free(temp);
}
void haar_transform_2d(double **image, int width, int height) {
// Transform rows
for (int i = 0; i < height; i++) {
haar_transform_1d(image[i], width);
}
// Transform columns
double *col = (double*)malloc(height * sizeof(double));
for (int j = 0; j < width; j++) {
for (int i = 0; i < height; i++) {
col[i] = image[i][j];
}
haar_transform_1d(col, height);
for (int i = 0; i < height; i++) {
image[i][j] = col[i];
}
}
free(col);
}
double compress_signal(double *signal, int n, double threshold) {
// Zero out small coefficients
int removed = 0;
for (int i = 0; i < n; i++) {
if (fabs(signal[i]) < threshold) {
signal[i] = 0.0;
removed++;
}
}
return removed / (double)n;
}
void generate_signal(double *signal, int n) {
unsigned int seed = 42;
for (int i = 0; i < n; i++) {
seed = seed * 1103515245 + 12345;
signal[i] = sin(2.0 * 3.14159 * i / 100.0) +
0.5 * sin(2.0 * 3.14159 * i / 20.0) +
0.1 * ((seed & 0xFFFF) / (double)0xFFFF - 0.5);
}
}
double compute_mse(double *signal1, double *signal2, int n) {
double sum = 0.0;
for (int i = 0; i < n; i++) {
double diff = signal1[i] - signal2[i];
sum += diff * diff;
}
return sum / n;
}
int main() {
double *signal = (double*)malloc(SIGNAL_SIZE * sizeof(double));
double *original = (double*)malloc(SIGNAL_SIZE * sizeof(double));
double *compressed = (double*)malloc(SIGNAL_SIZE * sizeof(double));
generate_signal(original, SIGNAL_SIZE);
clock_t start = clock();
double total_compression = 0.0;
double total_mse = 0.0;
for (int iter = 0; iter < NUM_TRANSFORMS; iter++) {
// Copy original
for (int i = 0; i < SIGNAL_SIZE; i++) {
signal[i] = original[i];
}
// Forward transform
haar_transform_1d(signal, SIGNAL_SIZE);
// Compress
for (int i = 0; i < SIGNAL_SIZE; i++) {
compressed[i] = signal[i];
}
double ratio = compress_signal(compressed, SIGNAL_SIZE, 0.1);
total_compression += ratio;
// Inverse transform
inverse_haar_transform_1d(compressed, SIGNAL_SIZE);
// Compute error
double mse = compute_mse(original, compressed, SIGNAL_SIZE);
total_mse += mse;
}
clock_t end = clock();
double time_spent = (double)(end - start) / CLOCKS_PER_SEC;
printf("Haar wavelet transform: signal=%d, %d transforms, %.6f seconds\n",
SIGNAL_SIZE, NUM_TRANSFORMS, time_spent);
printf("Average compression: %.2f%%, MSE: %.6f\n",
total_compression / NUM_TRANSFORMS * 100, total_mse / NUM_TRANSFORMS);
free(signal);
free(original);
free(compressed);
return 0;
}
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