c++实现巴特沃斯带通滤波器代码

巴特沃斯带通滤波器是一种常见的数字信号处理滤波器，可以用于滤除某些频率范围内的噪声信号，保留其他频率范围内的信号。下面是一份C语言实现的巴特沃斯带通滤波器代码示例：

#include <math.h>

#define PI 3.14159265358979323846

typedef struct {
    int order;          // 阶数
    float fc1;          // 通带截止频率1
    float fc2;          // 通带截止频率2
    float fs;           // 采样频率
    float a[10];        // 系数a
    float b[10];        // 系数b
} ButterworthFilter;

void butterworth_bandpass_init(ButterworthFilter *filter, int order, float fc1, float fc2, float fs) {
    filter->order = order;
    filter->fc1 = fc1;
    filter->fc2 = fc2;
    filter->fs = fs;
    float W1 = 2 * PI * fc1 / fs;
    float W2 = 2 * PI * fc2 / fs;
    float alpha1 = sin(W1) / (2 * order);
    float alpha2 = sin(W2) / (2 * order);
    float beta = cos((W1 + W2) / 2) / 2;
    float gamma = 1 / tan((W2 - W1) / 2);
    float a0 = 1 + alpha1;
    float b0 = 1 + alpha2;
    for (int i = 0; i < order; i++) {
        filter->a[i] = 2 * cos((2 * i + 1) * PI / (2 * order)) / a0;
        filter->b[i] = 2 * cos((2 * i + 1) * PI / (2 * order)) / b0;
    }
    filter->a[order] = (1 - alpha1) / a0;
    filter->b[order] = (1 - alpha2) / b0;
    filter->a[order + 1] = -beta * gamma / a0;
    filter->b[order + 1] = beta * gamma / b0;
    filter->a[order + 2] = -(1 - alpha1) / a0;
    filter->b[order + 2] = -(1 - alpha2) / b0;
    filter->a[order + 3] = 0;
    filter->b[order + 3] = 0;
}

float butterworth_bandpass_filter(ButterworthFilter *filter, float input) {
    float output = input;
    for (int i = 0; i < filter->order; i++) {
        float temp = output;
        output = filter->a[i] * output + filter->b[i] * filter->a[filter->order + i] - filter->b[filter->order + i] * filter->a[filter->order + i] + filter->b[filter->order + i] * temp;
    }
    return output;
}

使用方法：

int main() {
    ButterworthFilter filter;
    butterworth_bandpass_init(&filter, 4, 50, 100, 1000);
    float input = 0.0;
    float output = 0.0;
    for (int i = 0; i < 1000; i++) {
        output = butterworth_bandpass_filter(&filter, input);
        input = sin(2 * PI * 50 * i / 1000) + sin(2 * PI * 100 * i / 1000);
        printf("%f\n", output);
    }
    return 0;
}

在上面的例子中，初始化了一个4阶、通带截止频率为50Hz至100Hz、采样频率为1000Hz的巴特沃斯带通滤波器，并将输入信号设置为50Hz和100Hz的正弦波信号。使用`butterworth_bandpass_filter`函数对输入信号进行滤波，并打印输出信号。