脑电信号频域分析butterworth滤波器代码

以下是脑电信号频域分析butterworth滤波器代码的示例：

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

#define PI 3.14159265358979323846

void butterworth_filter(double *input, double *output, int n, double fc, int fs)
{
    double w = 2 * PI * fc / fs;
    double a = tan(w / 2);
    double a2 = a * a;
    double b = 1 / (1 + sqrt(2) * a + a2);
    double b1 = 2 * b;
    double b2 = b;
    double a1 = 2 * b * (a2 - 1);
    double a2 = b * (1 - sqrt(2) * a + a2);

    double x1 = , x2 = , y1 = , y2 = ;

    for (int i = ; i < n; i++) {
        output[i] = b * input[i] + b1 * x1 + b2 * x2 - a1 * y1 - a2 * y2;
        x2 = x1;
        x1 = input[i];
        y2 = y1;
        y1 = output[i];
    }
}

int main()
{
    int n = 100;
    double fs = 100;
    double fc = 50;
    double *input = (double *)malloc(n * sizeof(double));
    double *output = (double *)malloc(n * sizeof(double));

    for (int i = ; i < n; i++) {
        input[i] = sin(2 * PI * i * 10 / fs) + sin(2 * PI * i * 100 / fs);
    }

    butterworth_filter(input, output, n, fc, fs);

    for (int i = ; i < n; i++) {
        printf("%f\n", output[i]);
    }

    free(input);
    free(output);

    return ;
}