```cpp
#include <iostream>
#include <vector>
#include <cmath>
// 计算离散傅里叶变换（DFT）
std::vector<double> dft(const std::vector<double>& signal) {
int N = signal.size();
std::vector<double> result(N);
for (int k = 0; k < N; ++k) {
double sum = 0;
for (int n = 0; n < N; ++n) {
double angle = -2 * M_PI * k * n / N;
sum += signal[n] * std::cos(angle);
}
result[k] = sum;
}
return result;
}
// 通过预滤波器去除共振荡频率
std::vector<double> remove_coherent_noise(const std::vector<double>& signal, double threshold) {
std::vector<double> dft_result = dft(signal);
int N = signal.size();
for (int i = 1; i < N / 2; ++i) {
if (std::abs(dft_result[i]) > threshold) {
dft_result[i] = 0;
}
}
std::vector<double> filtered_signal(N);
for (int n = 0; n < N; ++n) {
double sum = 0;
for (int k = 0; k < N; ++k) {
double angle = 2 * M_PI * k * n / N;
sum += dft_result[k] * std::cos(angle);
}
filtered_signal[n] = sum;
}
return filtered_signal;
}
int main() {
std::vector<double> signal = {1, 2, 3, 4, 5, 6, 7, 8};
double threshold = 10;
std::vector<double> filtered_signal = remove_coherent_noise(signal, threshold);
for (double value : filtered_signal) {
std::cout << value << " ";
}
std::cout << std::endl;
return 0;
}
```
这段C++代码实现了一个通过轨道预滤波器在指令时去除导致振动的共振荡频率的功能。首先计算输入信号的离散傅里叶变换（DFT），然后根据阈值去除共振荡频率，最后通过逆DFT得到滤波后的信号。
