4阶巴特沃斯带通滤波器的C语言代码实现

以下是一个基于巴特沃斯滤波器的4阶带通滤波器的C语言代码实现：

#define M_PI 3.14159265358979323846

// 计算巴特沃斯滤波器系数
void butterworth_bandpass(int n, double lowcut, double highcut, int sampleRate, double *b, double *a) {
    double fn = sampleRate / 2.0;
    double w1 = 2 * M_PI * lowcut / fn;
    double w2 = 2 * M_PI * highcut / fn;
    double bw = w2 - w1;
    double gain = 1;
    double den, num, x;

    for (int i = 0; i < n; i++) {
        x = M_PI * (2.0 * i + 1.0) / (2.0 * n);
        den = 4.0 + 4.0 * sin(x) / bw + (1.0 / (gain * gain) - 2.0) * (1.0 + sin(x) / bw) * (1.0 + sin(x) / bw);
        num = (1.0 / (gain * gain)) * (1.0 + (2.0 * M_PI * w1 / fn) * sin(x)) * (1.0 + (2.0 * M_PI * w2 / fn) * sin(x));
        b[i] = num / den;
        if (i == 0) {
            a[i] = 1.0;
        } else {
            b[i] *= gain * gain;
            a[i] = (2.0 + 2.0 * sin(x) / bw + (1.0 / (gain * gain) - 2.0) * (1.0 + sin(x) / bw) * (1.0 + sin(x) / bw)) / den;
        }
    }
}

// 应用巴特沃斯滤波器
void apply_butterworth_bandpass(int n, double *input, double *output, double *b, double *a) {
    double *v = (double *)calloc(n, sizeof(double));
    for (int i = 0; i < n; i++) {
        output[i] = b[0] * input[i] + v[0];
        for (int j = 1; j < n; j++) {
            v[j - 1] = b[j] * input[i] - a[j] * output[i] + v[j];
        }
    }
    free(v);
}

其中，`n`表示滤波器的阶数，`lowcut`和`highcut`表示带通滤波器的下限和上限频率，`sampleRate`表示输入信号的采样率，`b`和`a`分别表示滤波器的分子和分母系数，`input`和`output`分别表示输入和输出信号。通过调用`butterworth_bandpass`函数来计算滤波器系数，然后通过调用`apply_butterworth_bandpass`函数来应用滤波器。