希尔伯特变换 实现C++
时间: 2023-07-11 13:24:01 浏览: 159
希尔伯特变换(Hilbert Transform)是一种数学变换,用于将信号从实数域转换到复数域。在信号处理中经常用到,例如在调制解调、滤波、频率分析等领域。
以下是一个简单的C++实现:
```c++
#include <complex>
#include <iostream>
#include <vector>
using namespace std;
void hilbert_transform(const vector<double>& x, vector<complex<double>>& y) {
int n = x.size();
vector<double> h(n), f(n);
h[0] = h[n / 2] = 1;
for (int i = 1; i < n / 2; i++) {
h[i] = 2;
}
for (int i = 0; i < n; i++) {
f[i] = 2 * M_PI / n * i;
}
vector<complex<double>> c(n);
for (int i = 0; i < n; i++) {
c[i] = complex<double>(x[i], 0);
}
vector<complex<double>> dft(n);
for (int i = 0; i < n; i++) {
complex<double> sum(0, 0);
for (int j = 0; j < n; j++) {
sum += c[j] * exp(complex<double>(0, -f[i] * j));
}
dft[i] = sum;
}
for (int i = 0; i < n; i++) {
dft[i] *= h[i];
}
for (int i = 0; i < n; i++) {
c[i] = complex<double>(0, 0);
for (int j = 0; j < n; j++) {
c[i] += dft[j] * exp(complex<double>(0, f[i] * j));
}
y[i] = c[i] / complex<double>(0, 1);
}
}
int main() {
vector<double> x = {1, 2, 3, 4, 5};
vector<complex<double>> y(x.size());
hilbert_transform(x, y);
for (int i = 0; i < x.size(); i++) {
cout << y[i].real() << " " << y[i].imag() << endl;
}
return 0;
}
```
这段代码使用了STL中的复数类型,以及使用了快速傅里叶变换来实现离散傅里叶变换。如果你不熟悉傅里叶变换,可以先了解一下这个概念。
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