用C语言实现一阶巴特沃斯高通滤波器

可以使用以下代码实现一阶巴特沃斯高通滤波器：

#include <stdio.h>
#include <math.h>

#define PI 3.14159265358979323846

double b0, b1, b2, a1, a2;

void butterworth_highpass(double fc, double fs, int order) {
    double wc = tan((PI * fc) / fs);
    double k = wc / (1 + wc);
    double k2 = k * k;
    double sqrt2 = sqrt(2.0);
    double sqrt2k = sqrt2 * k;
    double sqrt2k2 = sqrt2 * k2;
    double sqrt2kk2 = sqrt2 * k * k2;
    double sqrt2k2k2 = sqrt2 * k2 * k2;
    switch (order) {
        case 1:
            b0 = k;
            b1 = -k;
            a1 = -k + 1;
            break;
        case 2:
            b0 = k2;
            b1 = -2 * k2;
            b2 = k2;
            a1 = -2 * k + 2;
            a2 = -k2 + 2 * k - 1;
            break;
        case 3:
            b0 = k2 * sqrt2k;
            b1 = -2 * k2 * sqrt2k;
            b2 = k2 * sqrt2k;
            a1 = -2 * k * (1 + sqrt2k + k2);
            a2 = -(1 + sqrt2k2 + sqrt2kk2 + sqrt2k2k2);
            break;
        default:
            printf("Unsupported order %d\n", order);
            break;
    }
}

double filter(double x) {
    static double x1 = 0, x2 = 0, y1 = 0, y2 = 0;
    double y = b0 * x + b1 * x1 + b2 * x2 - a1 * y1 - a2 * y2;
    x2 = x1;
    x1 = x;
    y2 = y1;
    y1 = y;
    return y;
}

int main() {
    double fc = 1000; // 我们要实现的截止频率
    double fs = 44100; // 采样率
    int order = 2; // 阶数
    butterworth_highpass(fc, fs, order);
    // 现在我们可以使用 filter 函数来过滤信号了
    return 0;
}

这段代码实现了一个一阶、二阶或三阶的巴特沃斯高通滤波器，可以通过调整 `fc` 和 `order` 参数来控制截止频率和阶数。