C实现对复数数组fft后计算谱熵
时间: 2024-05-12 08:20:26 浏览: 12
以下是C语言实现对复数数组fft后计算谱熵的示例代码:
```
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define N 16 // FFT大小
#define PI 3.14159265358979323846
// 复数结构体
typedef struct {
double real;
double imag;
} Complex;
// 计算复数乘法
Complex complex_mul(Complex a, Complex b) {
Complex c;
c.real = a.real * b.real - a.imag * b.imag;
c.imag = a.real * b.imag + a.imag * b.real;
return c;
}
// 计算FFT
void fft(Complex *x, int n) {
if (n <= 1) {
return;
}
Complex *even = (Complex*)malloc(n / 2 * sizeof(Complex));
Complex *odd = (Complex*)malloc(n / 2 * sizeof(Complex));
for (int i = 0; i < n / 2; i++) {
even[i] = x[2 * i];
odd[i] = x[2 * i + 1];
}
fft(even, n / 2);
fft(odd, n / 2);
for (int k = 0; k < n / 2; k++) {
Complex t = complex_mul(odd[k], (Complex){cos(-2 * PI * k / n), sin(-2 * PI * k / n)});
x[k] = complex_mul((Complex){1, 0}, complex_mul(even[k], (Complex){1, 0}));
x[k + n / 2] = complex_mul((Complex){1, 0}, t);
x[k] = complex_mul(x[k], (Complex){1, 0});
x[k + n / 2] = complex_mul(x[k + n / 2], (Complex){1, 0});
}
free(even);
free(odd);
}
// 计算谱熵
double spectral_entropy(Complex *x, int n) {
double sum = 0.0;
double *p = (double*)malloc(n * sizeof(double));
for (int i = 0; i < n; i++) {
p[i] = x[i].real * x[i].real + x[i].imag * x[i].imag;
sum += p[i];
}
for (int i = 0; i < n; i++) {
p[i] /= sum;
}
double se = 0.0;
for (int i = 0; i < n; i++) {
if (p[i] > 0) {
se -= p[i] * log2(p[i]);
}
}
free(p);
return se;
}
int main() {
Complex x[N] = {{1, 0}, {2, 0}, {3, 0}, {4, 0}, {5, 0}, {6, 0}, {7, 0}, {8, 0},
{8, 0}, {7, 0}, {6, 0}, {5, 0}, {4, 0}, {3, 0}, {2, 0}, {1, 0}};
fft(x, N);
double se = spectral_entropy(x, N);
printf("Spectral entropy = %lf\n", se);
return 0;
}
```
在该示例代码中,使用了复数结构体来表示复数,包括实部和虚部。计算FFT的函数使用了递归算法,将输入数组划分为两个子数组,分别计算FFT后再合并。计算复数乘法的函数用于计算DFT和IDFT过程中的复数乘法。计算谱熵的函数使用了公式:$SE=-\sum_{i=1}^np_i\log_2p_i$,其中$p_i$表示第$i$个频率的幅度平方占总能量的比例,即概率分布。在主函数中,先将输入的复数数组进行FFT,再计算谱熵并输出结果。