C语言如何使用FFT
```#include <math.h>
#include <stdio.h>
#include <stdlib.h>
typedef struct {
double real;
double imag;
} complex;
// 复数加法
complex add(complex a, complex b) {
complex result;
result.real = a.real + b.real;
result.imag = a.imag + b.imag;
return result;
}
// 复数减法
complex subtract(complex a, complex b) {
complex result;
result.real = a.real - b.real;
result.imag = a.imag - b.imag;
return result;
}
// 复数乘法
complex multiply(complex a, complex b) {
complex result;
result.real = a.real * b.real - a.imag * b.imag;
result.imag = a.real * b.imag + a.imag * b.real;
return result;
}
// 检查是否为2的幂
int is_power_of_two(int n) {
return (n > 0) && ((n & (n - 1)) == 0);
}
// 位反转函数
unsigned int reverse_bits(unsigned int x, int log2n) {
unsigned int n = 0;
for (int i = 0; i < log2n; i++) {
n <<= 1;
n |= (x & 1);
x >>= 1;
}
return n;
}
// 位反转排列
void bit_reverse(complex *x, int n) {
int log2n = log2(n);
for (int i = 0; i < n; i++) {
int j = reverse_bits(i, log2n);
if (i < j) {
complex temp = x;
x = x;
x = temp;
}
}
}
// FFT函数
void fft(complex *x, int n) {
if (!is_power_of_two(n)) {
fprintf(stderr, "错误：输入长度必须是2的幂。\n");
return;
}
bit_reverse(x, n);
int log2n = log2(n);
for (int s = 1; s <= log2n; s++) {
int m = 1 << s; // 当前块大小：2^s
int half_m = m >> 1;
// 基础旋转因子：W_m = e^(-2πi/m)
double theta = -2 * M_PI / m;
complex w_m = {cos(theta), sin(theta)};
for (int k = 0; k < n; k += m) { // 处理每个块
complex w = {1.0, 0.0}; // W_m^0 = 1
for (int j = 0; j < half_m; j++) {
complex t = multiply(w, x);
complex u = x;
x = add(u, t);
x = subtract(u, t);
w = multiply(w, w_m); // 更新旋转因子：W_m^(j+1)
}
}
}
}
// 示例：计算4点FFT
int main() {
int n = 4;
complex x[] = {{1, 0}, {2, 0}, {3, 0}, {4, 0}};
fft(x, n);
printf("FFT结果：\n");
for (int i = 0; i < n; i++) {
printf("x[%d] = %.2f + %.2fi\n", i, x.real, x.imag);
}
return 0;
}
```
这种FFT是不是就是频谱显示可以使用？有进阶一些的吗，来点 C中一般有库可以直接使用吧
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