c++实现巴特沃斯带通滤波器
时间: 2023-05-30 10:07:43 浏览: 40
巴特沃斯带通滤波器是一种常见的数字滤波器,用于去除信号中的高频和低频成分,保留中间频率的信号。实现巴特沃斯带通滤波器可以采用以下步骤:
1. 确定滤波器的参数:包括截止频率、通带和阻带的衰减量等。
2. 计算滤波器的系数:可以使用巴特沃斯滤波器设计公式计算出滤波器的系数。
3. 实现滤波器:将滤波器系数应用到输入信号上,计算出输出信号。
以下是一个C语言实现巴特沃斯带通滤波器的示例代码:
```
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define PI 3.14159265358979323846
// 巴特沃斯滤波器设计函数
void butterworth_bandpass_filter(double *b, double *a, int order, double Wn1, double Wn2)
{
int i, j;
double bw, Wc1, Wc2;
double *p1, *p2, *p3;
double *alpha, *beta;
double *c, *d, *e, *f;
bw = Wn2 - Wn1;
Wc1 = 2 * PI * Wn1;
Wc2 = 2 * PI * Wn2;
alpha = (double *) malloc((order + 1) * sizeof(double));
beta = (double *) malloc((order + 1) * sizeof(double));
c = (double *) malloc((order + 1) * sizeof(double));
d = (double *) malloc((order + 1) * sizeof(double));
e = (double *) malloc((order + 1) * sizeof(double));
f = (double *) malloc((order + 1) * sizeof(double));
for (i = 1; i <= order; i++) {
p1 = alpha + i;
p2 = beta + i;
*p1 = sin((2 * i - 1) * PI / (2 * order));
*p1 = bw * 0.5 / *p1;
*p2 = 0.25 + 0.5 * sin((2 * i - 1) * PI / (2 * order));
*p2 = 1 - 2 * *p1 * Wc1 / *p2;
}
*a = 1;
for (i = 1; i <= order / 2; i++) {
c[i] = 0;
d[i] = 0;
p1 = alpha + 2 * i - 1;
p2 = beta + 2 * i - 1;
p3 = alpha + 2 * i;
*c *= *p2;
*d += *p1 * *p2;
*f += *p3 / *p2;
}
*b = (*c + *d) / (*f + 1);
for (i = 1; i <= order / 2; i++) {
c[i] = 1;
if (i == order / 2 && order % 2 == 1)
d[i] = alpha[order / 2 + 1];
else
d[i] = 0;
for (j = 1; j <= order / 2; j++) {
if (i == j)
continue;
p1 = alpha + i + j - 1;
p2 = beta + i + j - 1;
*c *= *p2;
*d += *p1 * *p2;
}
p1 = alpha + 2 * i - 1;
p2 = beta + 2 * i - 1;
p3 = alpha + 2 * i;
e[i] = (*c + *d) / (*p3 + *p2 * *b);
f[i] = (*p3 + *p2 * *b) / (*c + *d);
}
for (i = 1; i <= order / 2; i++) {
p1 = b + i;
p2 = a + i;
p3 = e + i;
*p1 = *p3;
*p2 = *p3 * f[i];
p1 = b + order - i + 1;
p2 = a + order - i + 1;
*p1 = *p3;
*p2 = *p3 * f[i];
}
if (order % 2 == 1) {
p1 = b + order / 2 + 1;
p2 = a + order / 2 + 1;
*p1 = e[order / 2 + 1];
*p2 = e[order / 2 + 1] * (1 / beta[order / 2 + 1]);
}
free(alpha);
free(beta);
free(c);
free(d);
free(e);
free(f);
}
// 实现带通滤波器
void bandpass_filter(double *x, double *y, int len, double *b, double *a, int order)
{
int i, j;
double *buf_x, *buf_y;
buf_x = (double *) calloc(order + 1, sizeof(double));
buf_y = (double *) calloc(order + 1, sizeof(double));
for (i = 0; i < len; i++) {
buf_x[0] = x[i];
y[i] = b[0] * buf_x[0];
for (j = 1; j <= order; j++) {
buf_y[j] = buf_y[j - 1] + b[j] * buf_x[j] - a[j] * y[i - j];
buf_x[j] = buf_x[j - 1];
}
y[i] += buf_y[order];
}
free(buf_x);
free(buf_y);
}
int main()
{
int i, len, order;
double *x, *y;
double Wn1, Wn2;
double *b, *a;
// 读入数据
printf("请输入信号长度:");
scanf("%d", &len);
x = (double *) malloc(len * sizeof(double));
y = (double *) malloc(len * sizeof(double));
printf("请输入信号数据:");
for (i = 0; i < len; i++) {
scanf("%lf", &x[i]);
}
// 设计滤波器
printf("请输入滤波器阶数:");
scanf("%d", &order);
b = (double *) malloc((order + 1) * sizeof(double));
a = (double *) malloc((order + 1) * sizeof(double));
printf("请输入截止频率范围(单位:Hz):");
scanf("%lf%lf", &Wn1, &Wn2);
butterworth_bandpass_filter(b, a, order, Wn1, Wn2);
// 滤波
bandpass_filter(x, y, len, b, a, order);
// 输出结果
printf("滤波前的信号:");
for (i = 0; i < len; i++) {
printf("%lf ", x[i]);
}
printf("\n");
printf("滤波后的信号:");
for (i = 0; i < len; i++) {
printf("%lf ", y[i]);
}
printf("\n");
free(x);
free(y);
free(b);
free(a);
return 0;
}
```
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