用c++编写fft函数,实现快速傅里叶算法,要求算法速度尽可能快
时间: 2024-02-11 15:07:37 浏览: 21
好的,下面是一个用C++实现的快速傅里叶变换算法FFT:
```cpp
#include <complex>
#include <cmath>
#include <vector>
using namespace std;
const double PI = acos(-1);
typedef complex<double> Complex;
void fft(vector<Complex>& a, bool inverse) {
int n = a.size();
for (int i = 1, j = 0; i < n; i++) {
int bit = n >> 1;
for (; j >= bit; bit >>= 1) {
j -= bit;
}
j += bit;
if (i < j) {
swap(a[i], a[j]);
}
}
for (int len = 2; len <= n; len <<= 1) {
double ang = 2 * PI / len;
if (inverse) {
ang = -ang;
}
Complex wlen(cos(ang), sin(ang));
for (int i = 0; i < n; i += len) {
Complex w(1);
for (int j = 0; j < len / 2; j++) {
Complex u = a[i + j];
Complex t = w * a[i + j + len / 2];
a[i + j] = u + t;
a[i + j + len / 2] = u - t;
w *= wlen;
}
}
}
if (inverse) {
for (int i = 0; i < n; i++) {
a[i] /= n;
}
}
}
vector<double> convolve(const vector<double>& a, const vector<double>& b) {
int n = 1;
while (n < a.size() + b.size()) {
n <<= 1;
}
vector<Complex> fa(n);
for (int i = 0; i < a.size(); i++) {
fa[i] = a[i];
}
vector<Complex> fb(n);
for (int i = 0; i < b.size(); i++) {
fb[i] = b[i];
}
fft(fa, false);
fft(fb, false);
for (int i = 0; i < n; i++) {
fa[i] *= fb[i];
}
fft(fa, true);
vector<double> result(n);
for (int i = 0; i < n; i++) {
result[i] = fa[i].real();
}
return result;
}
```
这里实现了一个convolve函数,可以计算两个多项式的卷积。使用FFT算法的时间复杂度为O(nlogn),比传统的O(n^2)卷积算法要快得多。