编写一个快速傅里叶变换(FFT)c语言程序,
时间: 2023-08-31 13:37:55 浏览: 75
### 回答1:
我可以为您提供一个示例代码,用于编写快速傅里叶变换(FFT)的C语言程序: #include <stdio.h>
#include <stdlib.h>
#include <math.h> void FFT(double *Rdat, double *Idat, int N, int LogN, int FFT_FORWARD)
{
int n, k, io, ie, in, i;
double ru, iu, rtp, itp, rtq, itq, rw, iw, sr; /* Calculation of the coefficients */
io = 0;
for (n=1; n<=LogN; n++)
{
ie = (int)pow(2,n);
ru = cos(M_PI/ie);
iu = sin(M_PI/ie);
rw = 1;
iw = 0;
in = io + ie;
for (k=io; k<in; k++)
{
for (i=k; i<2*N; i+=in)
{
rtp = Rdat[i];
itp = Idat[i];
rtq = Rdat[i+ie];
itq = Idat[i+ie];
Rdat[i] = rtp + rtq;
Idat[i] = itp + itq;
Rdat[i+ie] = rtp - rtq;
Idat[i+ie] = itp - itq;
if (FFT_FORWARD)
{
sr = rw*Rdat[i+ie] - iw*Idat[i+ie];
Idat[i+ie] = iw*Rdat[i+ie] + rw*Idat[i+ie];
Rdat[i+ie] = sr;
}
}
sr = rw;
rw = rw*ru - iw*iu;
iw = iw*ru + sr*iu;
}
io = in;
} /* Reordering of the coefficients */
n = N;
k = 0;
while (n > 1)
{
int m;
m = (int)pow(2, LogN-k-1);
for (i=0; i<N; i+=n)
{
int j;
for (j=i; j<i+m; j++)
{
sr = Rdat[j+m];
Rdat[j+m] = Rdat[j] - sr;
Rdat[j] = Rdat[j] + sr;
sr = Idat[j+m];
Idat[j+m] = Idat[j] - sr;
Idat[j] = Idat[j] + sr;
}
}
n = m;
k = k+1;
}
}
### 回答2:
快速傅里叶变换(FFT)是一种高效的离散傅里叶变换(DFT)算法,用于将一个离散时间域信号转换为频域表示。以下是一个用C语言编写的简单FFT程序示例:
```c
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
// 计算复数的乘积
void complexMultiply(float real1, float imag1, float real2, float imag2, float *realResult, float *imagResult) {
*realResult = real1 * real2 - imag1 * imag2;
*imagResult = real1 * imag2 + real2 * imag1;
}
// 执行FFT
void performFft(float* realIn, float* imagIn, float* realOut, float* imagOut, int n) {
if (n == 1) {
realOut[0] = realIn[0];
imagOut[0] = imagIn[0];
return;
}
float* realEven = (float*)malloc(n / 2 * sizeof(float));
float* imagEven = (float*)malloc(n / 2 * sizeof(float));
float* realOdd = (float*)malloc(n / 2 * sizeof(float));
float* imagOdd = (float*)malloc(n / 2 * sizeof(float));
for (int i = 0; i < n / 2; i++) {
realEven[i] = realIn[i * 2];
imagEven[i] = imagIn[i * 2];
realOdd[i] = realIn[i * 2 + 1];
imagOdd[i] = imagIn[i * 2 + 1];
}
float* realFftEven = (float*)malloc(n / 2 * sizeof(float));
float* imagFftEven = (float*)malloc(n / 2 * sizeof(float));
float* realFftOdd = (float*)malloc(n / 2 * sizeof(float));
float* imagFftOdd = (float*)malloc(n / 2 * sizeof(float));
performFft(realEven, imagEven, realFftEven, imagFftEven, n / 2);
performFft(realOdd, imagOdd, realFftOdd, imagFftOdd, n / 2);
for (int k = 0; k < n / 2; k++) {
float angle = -2 * M_PI * k / n;
float cosA = cos(angle);
float sinA = sin(angle);
float realTmp = realFftOdd[k] * cosA - imagFftOdd[k] * sinA;
float imagTmp = realFftOdd[k] * sinA + imagFftOdd[k] * cosA;
realOut[k] = realFftEven[k] + realTmp;
imagOut[k] = imagFftEven[k] + imagTmp;
realOut[k + n / 2] = realFftEven[k] - realTmp;
imagOut[k + n / 2] = imagFftEven[k] - imagTmp;
}
free(realEven);
free(imagEven);
free(realOdd);
free(imagOdd);
free(realFftEven);
free(imagFftEven);
free(realFftOdd);
free(imagFftOdd);
}
int main() {
int n = 16;
float* realIn = (float*)malloc(n * sizeof(float));
float* imagIn = (float*)malloc(n * sizeof(float));
for (int i = 0; i < n; i++) {
realIn[i] = i + 1;
imagIn[i] = 0;
}
float* realOut = (float*)malloc(n * sizeof(float));
float* imagOut = (float*)malloc(n * sizeof(float));
performFft(realIn, imagIn, realOut, imagOut, n);
printf("FFT结果:\n");
for (int i = 0; i < n; i++) {
printf("%.2f + %.2fi\n", realOut[i], imagOut[i]);
}
free(realIn);
free(imagIn);
free(realOut);
free(imagOut);
return 0;
}
```
这个程序可以计算给定输入序列的FFT,并打印出结果。程序首先定义了一个复数乘法函数`complexMultiply`,用于计算两个复数的乘积。然后,定义了一个执行FFT的函数`performFft`,使用递归的方式将输入序列划分为两个子序列,并对其执行FFT。最后,在`main`函数中,初始化了一个长度为16的输入序列,并调用`performFft`计算FFT结果,最后打印出结果。
请注意,这只是一个简单的FFT程序示例,并没有包含一些优化技术,如位反转、零填充等。在实际应用中,为了提高计算效率,可能需要进行更多的优化工作。