8阶巴特沃斯a和b系数可调的带通滤波器C语言代码

以下是一个可以调整a、b系数的8阶巴特沃斯带通滤波器的C语言代码：

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

#define PI 3.1415926535897932384626433832795

double *b, *a; // 巴特沃斯滤波器的b系数和a系数
double *x, *y; // 输入和输出缓冲区
double f1, f2, fs, fn; // 低通滤波器的截止频率和采样频率

double filter(double *x, double *y, int n)
{
    double output = 0;
    int i;

    for (i = 0; i <= 8; i++) {
        output += b[i] * x[n-i] - a[i+1] * y[n-i-1];
    }

    y[n] = output;
    return output;
}

void init_filter()
{
    int i;
    double t, alpha;

    // 计算归一化频率
    f1 = f1 / fn;
    f2 = f2 / fn;

    // 计算巴特沃斯滤波器的b系数
    for (i = 0; i <= 8; i++) {
        if (i == 4) {
            b[i] = (f2 - f1) / PI;
        } else {
            t = (double)(2*i - 8);
            b[i] = (sin(PI*f2*t) - sin(PI*f1*t)) / (PI*t);
        }
    }

    // 计算巴特沃斯滤波器的a系数
    alpha = exp(-PI * (f2 - f1) / sqrt(2.0));
    a[0] = 1.0;
    a[1] = -8.0 * alpha;
    a[2] = 28.0 * pow(alpha, 2.0) - 8.0 * alpha;
    a[3] = -56.0 * pow(alpha, 3.0) + 28.0 * pow(alpha, 2.0) - 8.0 * alpha;
    a[4] = 70.0 * pow(alpha, 4.0) - 56.0 * pow(alpha, 3.0) + 28.0 * pow(alpha, 2.0) - 8.0 * alpha;
    a[5] = -56.0 * pow(alpha, 5.0) + 70.0 * pow(alpha, 4.0) - 56.0 * pow(alpha, 3.0) + 28.0 * pow(alpha, 2.0) - 8.0 * alpha;
    a[6] = 28.0 * pow(alpha, 6.0) - 56.0 * pow(alpha, 5.0) + 70.0 * pow(alpha, 4.0) - 56.0 * pow(alpha, 3.0) + 28.0 * pow(alpha, 2.0) - 8.0 * alpha;
    a[7] = -8.0 * pow(alpha, 7.0) + 28.0 * pow(alpha, 6.0) - 56.0 * pow(alpha, 5.0) + 70.0 * pow(alpha, 4.0) - 56.0 * pow(alpha, 3.0) + 28.0 * pow(alpha, 2.0) - 8.0 * alpha;
    a[8] = pow(alpha, 8.0) - 8.0 * pow(alpha, 7.0) + 28.0 * pow(alpha, 6.0) - 56.0 * pow(alpha, 5.0) + 70.0 * pow(alpha, 4.0) - 56.0 * pow(alpha, 3.0) + 28.0 * pow(alpha, 2.0) - 8.0 * alpha;

    // 初始化输入和输出缓冲区
    for (i = 0; i <= 8; i++) {
        x[i] = 0;
        y[i] = 0;
    }
}

int main()
{
    int i, n, num;
    double input, output;

    // 输入参数
    printf("Enter the sampling frequency (in Hz): ");
    scanf("%lf", &fs);
    printf("\nEnter the low cutoff frequency (in Hz): ");
    scanf("%lf", &f1);
    printf("\nEnter the high cutoff frequency (in Hz): ");
    scanf("%lf", &f2);
    printf("\nEnter the number of samples: ");
    scanf("%d", &num);

    fn = fs / 2; // 计算Nyquist频率

    // 分配内存
    b = (double*)malloc(9 * sizeof(double));
    a = (double*)malloc(9 * sizeof(double));
    x = (double*)malloc(num * sizeof(double));
    y = (double*)malloc(num * sizeof(double));

    // 初始化滤波器
    init_filter();

    // 读入输入信号，进行滤波
    for (n = 0; n < num; n++) {
        scanf("%lf", &input);
        x[n] = input;
        output = filter(x, y, n);
        printf("%lf\n", output);
    }

    // 释放内存
    free(b);
    free(a);
    free(x);
    free(y);

    return 0;
}

在这个代码中，`b`和`a`是巴特沃斯滤波器的b系数和a系数，`x`和`y`是输入和输出缓冲区。`filter()`函数是巴特沃斯滤波器的实现函数，`init_filter()`函数用于计算b系数和a系数，并初始化缓冲区。`main()`函数中包含了输入参数、分配内存、初始化滤波器和进行滤波的过程。请注意，这个代码中使用了指针和动态内存分配，需要注意内存的释放。