巴特沃斯滤波器 c语言

巴特沃斯滤波器是数字信号处理中常用的一种滤波器，可以实现对数字信号的滤波。下面是一个巴特沃斯滤波器的C语言实现：

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

#define MAX_ORDER 8

typedef struct {
    int order;
    double a[MAX_ORDER + 1];
    double b[MAX_ORDER + 1];
} ButterworthFilter;

void butterworthFilterInit(ButterworthFilter *filter, int order, double cutoff_freq, double sample_rate) {
    int i;
    double theta;
    double q;
    double a[MAX_ORDER + 1];
    double b[MAX_ORDER + 1];
    double alpha[MAX_ORDER + 1];
    double beta[MAX_ORDER + 1];

    if (order < 1 || order > MAX_ORDER) {
        fprintf(stderr, "Error: Invalid filter order (%d)\n", order);
        exit(EXIT_FAILURE);
    }

    if (cutoff_freq <= 0.0 || cutoff_freq >= sample_rate / 2.0) {
        fprintf(stderr, "Error: Invalid cutoff frequency (%g)\n", cutoff_freq);
        exit(EXIT_FAILURE);
    }

    theta = M_PI * cutoff_freq / sample_rate;
    q = 1.0 / tan(theta);

    for (i = 0; i <= order; i++) {
        alpha[i] = sin((2.0 * i + 1.0) * M_PI / (2.0 * order));
        beta[i] = 1.0 + q * alpha[i];
    }

    b[0] = q / beta[0];
    a[0] = 1.0;

    for (i = 1; i <= order; i++) {
        b[i] = q * alpha[i] / beta[i];
        a[i] = (q * alpha[i - 1]) / beta[i] + (1.0 - q / beta[i - 1]);
    }

    filter->order = order;
    for (i = 0; i <= order; i++) {
        filter->a[i] = a[i];
        filter->b[i] = b[i];
    }
}

double butterworthFilterApply(ButterworthFilter *filter, double x) {
    int i;
    double y;

    y = filter->b[0] * x + filter->b[1] * filter->a[0] - filter->a[1] * filter->b[0];
    for (i = 2; i <= filter->order; i++) {
        y = filter->b[i - 1] * filter->a[i - 2] + filter->b[i] * filter->a[i - 1] - filter->a[i] * y;
    }

    return y;
}

int main(void) {
    int i;
    ButterworthFilter filter;
    double cutoff_freq = 1000.0;
    double sample_rate = 44100.0;
    double x[] = {1.0, 2.0, 3.0, 4.0, 5.0};
    double y;

    butterworthFilterInit(&filter, 4, cutoff_freq, sample_rate);

    for (i = 0; i < sizeof(x) / sizeof(x[0]); i++) {
        y = butterworthFilterApply(&filter, x[i]);
        printf("%g -> %g\n", x[i], y);
    }

    return EXIT_SUCCESS;
}

该实现中定义了一个ButterworthFilter结构体来存储滤波器的参数，其中包括滤波器的阶数、系数a和系数b。在初始化函数butterworthFilterInit中，根据滤波器的阶数、截止频率和采样率计算出系数a和系数b。在应用滤波器时，将输入信号x作为参数传入butterworthFilterApply函数中，计算得到输出信号y，并返回给调用者。

在main函数中，首先初始化一个ButterworthFilter结构体并设置滤波器的阶数、截止频率和采样率。然后将输入信号x作为参数传入butterworthFilterApply函数中，得到输出信号y，并打印输出。