用c语言设计一个二阶滤波器

下面是一个二阶低通滤波器的C代码示例：

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

#define PI 3.1415926

/* 定义二阶低通滤波器结构体 */
typedef struct {
    double a0, a1, a2;
    double b0, b1, b2;
    double x1, x2;
    double y1, y2;
} SecondOrderFilter;

/* 初始化二阶低通滤波器 */
void initFilter(SecondOrderFilter *filter, double f0, double fs) {
    double w0 = 2 * PI * f0 / fs;
    double cosw0 = cos(w0);
    double sinw0 = sin(w0);
    double alpha = sinw0 / (2 * 0.707);

    filter->a0 = 1 + alpha;
    filter->a1 = -2 * cosw0;
    filter->a2 = 1 - alpha;
    filter->b0 = (1 - cosw0) / 2;
    filter->b1 = 1 - cosw0;
    filter->b2 = (1 - cosw0) / 2;
    filter->x1 = 0;
    filter->x2 = 0;
    filter->y1 = 0;
    filter->y2 = 0;
}

/* 二阶低通滤波器处理 */
double processFilter(SecondOrderFilter *filter, double input) {
    double output = filter->b0 / filter->a0 * input
                  + filter->b1 / filter->a0 * filter->x1
                  + filter->b2 / filter->a0 * filter->x2
                  - filter->a1 / filter->a0 * filter->y1
                  - filter->a2 / filter->a0 * filter->y2;

    filter->x2 = filter->x1;
    filter->x1 = input;
    filter->y2 = filter->y1;
    filter->y1 = output;

    return output;
}

/* 测试代码 */
int main() {
    double f0 = 100;    /* 截止频率 */
    double fs = 1000;   /* 采样率 */
    double t = 0;       /* 当前时间 */
    double dt = 1 / fs; /* 采样间隔 */
    double input = 0;   /* 输入信号 */
    double output = 0;  /* 输出信号 */

    SecondOrderFilter filter;

    initFilter(&filter, f0, fs);

    /* 生成输入信号 */
    for (int i = 0; i < 1000; i++) {
        input = sin(2 * PI * 10 * t) + sin(2 * PI * 100 * t);
        output = processFilter(&filter, input);
        printf("%f,%f,%f\n", t, input, output);
        t += dt;
    }

    return 0;
}

该代码中，我们定义了一个二阶低通滤波器结构体 `SecondOrderFilter`，包含了滤波器的系数和历史输入输出值。函数 `initFilter` 用于初始化滤波器，输入截止频率 `f0` 和采样率 `fs`，根据公式计算出滤波器的系数。函数 `processFilter` 用于处理输入信号，根据滤波器的差分方程计算出输出信号，并更新历史输入输出值。

在测试代码中，我们生成了一个由两个正弦波叠加而成的输入信号，并通过 `processFilter` 函数进行滤波处理，输出结果包含时间、输入信号和输出信号。