```cpp

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// 计算离散傅里叶变换（DFT）

std::vector dft(const std::vector& signal) {

    int N = signal.size();

    std::vector 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 remove_coherent_noise(const std::vector& signal, double threshold) {

    std::vector 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 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 signal = {1, 2, 3, 4, 5, 6, 7, 8};

    double threshold = 10;

    std::vector filtered_signal = remove_coherent_noise(signal, threshold);

    for (double value : filtered_signal) {

        std::cout << value << " ";

    }

    std::cout << std::endl;

    return 0;