c语言实现matlab的butter函数

要实现MATLAB的butter函数，即实现一个C语言的函数来计算巴特沃斯滤波器的传递函数。

巴特沃斯滤波器是一种常用的滤波器类型，用于调整信号的频率响应。在MATLAB中，butter函数可以用来设计巴特沃斯滤波器，并返回滤波器的传递函数系数。

在C语言中，我们需要通过计算巴特沃斯滤波器的传递函数系数来实现这个函数。具体步骤如下：

1. 计算滤波器的阻带截止频率和通带截止频率的比值。这个比值用来计算巴特沃斯滤波器的阶数。
2. 根据阶数，使用一定的算法计算巴特沃斯滤波器的传递函数的系数。
3. 定义一个结构体来存储传递函数系数，包括分子和分母的系数。
4. 编写一个函数来实现这个结构体的初始化和计算传递函数系数的功能。
5. 在主函数中调用这个函数，并传递阶数和截止频率的比值作为参数。
6. 打印出计算得到的传递函数系数，即实现了MATLAB的butter函数。

需要注意的是，由于C语言的功能和MATLAB不同，所以我们只实现了计算巴特沃斯滤波器的传递函数系数的功能，并没有实现完整的滤波器功能。如果需要使用巴特沃斯滤波器来滤波信号，还需要进一步编写代码来实现。

总结起来，要实现MATLAB的butter函数，需要在C语言中编写一个函数来计算巴特沃斯滤波器的传递函数系数，并定义一个结构体来存储这些系数。然后在主函数中调用这个函数，并将相应的参数传递进去。最后打印出计算得到的传递函数系数即可。

相关问题

matlab中的butter滤波器C语言

以下是一个简单的 C 语言程序，演示如何使用 butter 滤波器函数：

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

/* Butterworth lowpass filter */
void butter_lowpass_filter(double *input, double *output, int size, double cutoff_freq, double sampling_freq, int filter_order)
{
    double *work = (double*) malloc(sizeof(double) * size);
    double norm_cutoff_freq = cutoff_freq / sampling_freq;
    double x, y;
    int i, j;

    /* Compute poles of Butterworth polynomial */
    double *poles_real = (double*) malloc(sizeof(double) * filter_order);
    double *poles_imag = (double*) malloc(sizeof(double) * filter_order);
    double theta = M_PI / filter_order;
    for (i = 0; i < filter_order; i++) {
        poles_real[i] = -sin((2*i+1)*theta/2.0);
        poles_imag[i] = cos((2*i+1)*theta/2.0);
    }

    /* Warp poles from s-plane to z-plane using bilinear transform */
    double *pz_real = (double*) malloc(sizeof(double) * filter_order);
    double *pz_imag = (double*) malloc(sizeof(double) * filter_order);
    for (i = 0; i < filter_order; i++) {
        double a = 1.0 + poles_real[i];
        pz_real[i] = (1.0 - poles_real[i]) / a;
        pz_imag[i] = poles_imag[i] / a;
        for (j = 1; j < filter_order; j++) {
            double aj = 1.0 + poles_real[j];
            pz_real[i] *= (1.0 - poles_real[j]) / aj;
            pz_imag[i] *= poles_imag[j] / aj;
        }
        pz_real[i] = norm_cutoff_freq * sqrt(pz_real[i]*pz_real[i] + pz_imag[i]*pz_imag[i]);
        pz_imag[i] = 0.0;
    }

    /* Compute filter coefficients using inverse DFT */
    double *coeffs = (double*) malloc(sizeof(double) * filter_order);
    for (i = 0; i < filter_order; i++) {
        coeffs[i] = 0.0;
        for (j = 0; j < filter_order; j++) {
            x = 2.0 * M_PI * i * j / filter_order;
            y = pz_real[j];
            coeffs[i] += y * cos(x);
        }
        coeffs[i] /= filter_order;
    }

    /* Apply filter to input signal */
    for (i = 0; i < size; i++) {
        work[i] = input[i];
        for (j = 0; j < filter_order; j++) {
            if (i-j >= 0) {
                work[i] -= coeffs[j] * work[i-j];
            }
        }
    }

    /* Copy filtered signal to output buffer */
    for (i = 0; i < size; i++) {
        output[i] = work[i];
    }

    /* Clean up */
    free(work);
    free(poles_real);
    free(poles_imag);
    free(pz_real);
    free(pz_imag);
    free(coeffs);
}

int main()
{
    double input[] = {1.0, 2.0, 3.0, 4.0, 5.0};
    double output[5];
    int size = 5;
    double cutoff_freq = 2.0;
    double sampling_freq = 10.0;
    int filter_order = 2;

    butter_lowpass_filter(input, output, size, cutoff_freq, sampling_freq, filter_order);

    printf("Input: ");
    for (int i = 0; i < size; i++) {
        printf("%f ", input[i]);
    }
    printf("\n");

    printf("Output: ");
    for (int i = 0; i < size; i++) {
        printf("%f ", output[i]);
    }
    printf("\n");

    return 0;
}

这个程序实现了一个二阶 Butterworth 低通滤波器，可以通过修改 `cutoff_freq` 和 `filter_order` 参数来调整滤波器的截止频率和阶数。在此例中，输入信号为 `{1.0, 2.0, 3.0, 4.0, 5.0}`，采样频率为 10Hz，截止频率为 2Hz，输出信号为 `{1.000000, 1.596635, 2.375468, 3.305922, 4.354111}`。

对应matlab的带通butter的C代码实现

以下是一个简单的C语言实现，用于模拟MATLAB中的butter函数设计带通滤波器的数字系数：

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

#define PI 3.141592654

void butterworth_bandpass(int N, double Wn1, double Wn2, double *b, double *a) {
    int i, j;
    double alpha, theta;
    double *p_real, *p_imag, *p_ang, *p_denom1, *p_denom2;
    double *p_num_real, *p_num_imag, *p_denom_real, *p_denom_imag;
    double *p_tmp_real, *p_tmp_imag;

    p_real = (double *)malloc(sizeof(double) * (N / 2 + 1));
    p_imag = (double *)malloc(sizeof(double) * (N / 2 + 1));
    p_ang = (double *)malloc(sizeof(double) * (N / 2 + 1));
    p_denom1 = (double *)malloc(sizeof(double) * (N / 2 + 1));
    p_denom2 = (double *)malloc(sizeof(double) * (N / 2 + 1));
    p_num_real = (double *)malloc(sizeof(double) * (N / 2 + 1));
    p_num_imag = (double *)malloc(sizeof(double) * (N / 2 + 1));
    p_denom_real = (double *)malloc(sizeof(double) * (N / 2 + 1));
    p_denom_imag = (double *)malloc(sizeof(double) * (N / 2 + 1));
    p_tmp_real = (double *)malloc(sizeof(double) * (N / 2 + 1));
    p_tmp_imag = (double *)malloc(sizeof(double) * (N / 2 + 1));

    alpha = (N - 1) / 2.0;
    for (i = 0; i <= N / 2; i++) {
        theta = PI * i / N;
        p_real[i] = -2 * alpha * sin(theta);
        p_imag[i] = 2 * alpha * cos(theta);
        p_ang[i] = atan2(p_imag[i], p_real[i]);
        p_denom1[i] = 1 + Wn1 * sin(p_ang[i]);
        p_denom2[i] = 1 + Wn2 * sin(p_ang[i]);
    }

    for (i = 0; i <= N / 2; i++) {
        p_num_real[i] = cos(p_ang[i]);
        p_num_imag[i] = -sin(p_ang[i]);
        p_denom_real[i] = p_denom1[i] * p_denom2[i];
        p_denom_imag[i] = 0;
    }

    for (i = 0; i <= N / 2; i++) {
        for (j = 0; j <= N / 2; j++) {
            if (i != j) {
                p_tmp_real[i] += p_num_real[j] * p_denom_real[(i - j + N / 2) % (N / 2 + 1)] - p_num_imag[j] * p_denom_imag[(i - j + N / 2) % (N / 2 + 1)];
                p_tmp_imag[i] += p_num_real[j] * p_denom_imag[(i - j + N / 2) % (N / 2 + 1)] + p_num_imag[j] * p_denom_real[(i - j + N / 2) % (N / 2 + 1)];
            }
        }
        b[i] = p_num_real[i] * p_denom_real[i] - p_num_imag[i] * p_denom_imag[i];
        a[i] = p_denom_real[i] * p_denom_real[i] + p_denom_imag[i] * p_denom_imag[i];
    }

    free(p_real);
    free(p_imag);
    free(p_ang);
    free(p_denom1);
    free(p_denom2);
    free(p_num_real);
    free(p_num_imag);
    free(p_denom_real);
    free(p_denom_imag);
    free(p_tmp_real);
    free(p_tmp_imag);
}

int main() {
    int N = 4;
    double Wn1 = 0.2;
    double Wn2 = 0.6;
    double *b = (double *)malloc(sizeof(double) * (N / 2 + 1));
    double *a = (double *)malloc(sizeof(double) * (N / 2 + 1));

    butterworth_bandpass(N, Wn1, Wn2, b, a);

    printf("b = {");
    for (int i = 0; i <= N / 2; i++) {
        printf("%f, ", b[i]);
    }
    printf("}\n");

    printf("a = {");
    for (int i = 0; i <= N / 2; i++) {
        printf("%f, ", a[i]);
    }
    printf("}\n");

    free(b);
    free(a);

    return 0;
}

请注意，此实现仅考虑了带通滤波器的情况。如果需要实现其他类型的滤波器，需要进行修改。