粉红噪声发生器

Definition of pinknoise

Pink noise or  1⁄f noise is a signal or process with a frequency spectrum such that the power spectral density (energy or power per frequency interval) is inversely proportional to the frequency of the signal. In pink noise, each octave (halving/doubling in frequency) carries an equal amount of noise energy. The name arises from the pink appearance of visible light with this power spectrum1.

Generate pink noise in MATLAB

使用MALTLAB提供的dsp.ColoredNoise System object 函数，系数alpha分别取0/1/2/-1/-2，可分别生成白噪/粉噪/棕噪/蓝噪/紫噪。函数调用方法可参考函数dsp.ColoredNoise。

Pinknosie generation algorithm：

这一段为MATLAB帮助文档给出的算法：

也就是说，给一段白噪声，将白噪声通过一个63阶的全极点滤波器，就可以得到粉噪。至于为什么这样可以的到粉噪，接下来会有专门的讲解。这里先说思路。
那么dsp.ColoredNoise这个函数实现粉噪发生器就可以分成这样两步：
Step1: 生成一段白噪声
x = wgn(0, 1, 100);
Step2:将白噪声通过63阶全极点滤波器滤波
y = filter(1, a, x);

在C语言里面，就可以利用这个思路来写Pinknoise发生器。

C implementation of Pinknoise

接下来的事情就非常简单，用C语言写一个粉噪发生器：

float x[N];
float y[N];

void print_array_to_file(FILE *fp, const float *x, int n)
{
    int i;

    for (i = 0; i < n; i++)    
        fprintf(fp, "%.15f\n", x[i]);
}

void white_noise(float *x, int n) 
{
    int i;

    for (i = 0; i < n; i++)    
        x[i] = 2.0f * rand() / RAND_MAX - 1.0f;
}

void invfreq_coeffs(float* coeffs, float alpha, int n)
{    
    float a = -alpha / 2.0f;

    coeffs[0] = a;

    int i;

    for (i = 1; i < n; i++)
        coeffs[i] = coeffs[i-1] / (i+1) * (i+a);
}

float allpole_filter(float  x,     // Input signal
               const float *a,     // Feedback coefficients
                     float *s,     // Delayline
                       int  p)     // Number of coefficients
{
    float y = x;

    int i;

    for (i = 0; i < p; i++)
        y -= a[i] * s[i];

    for (i = p - 1; i > 0; i--)
        s[i] = s[i-1];

    s[0] = y;

    return y;
}

void pinknoise(const float *x,  // Input signal  
                     float *y,  // Output signal
               const float *a,  // Feedback coefficients
                     float *s,  // Delayline
                       int  n,  // Sample points
                       int  p)  // Number of coefficients
{
    int i;

    for(i = 0; i < n; i++)
        y[i] = allpole_filter(x[i], a, s, p);
}               

int main(void)
{
    // 1. Generate white noise signal.
    white_noise(x, N);

    // 2. Generate pink noise filter coefficients.
    float coeffs[P];

    float alpha = 1.0f;

    float s[P];

    int i;
    for (i = 0; i < P; i++)
        s[i] = 0.0f;

    invfreq_coeffs(coeffs, alpha, P);

    // 3. Get pink noise signal by filtering the white noise signal.      
    pinknoise(x, y, coeffs, s, N, P);

    // 4. Save pink noise signal to file and verify it in MATLAB.
    FILE *fpx = fopen("whitenosie.txt", "w");

    FILE *fpy = fopen("pinknosie.txt", "w");

    FILE *fpa = fopen("coeffs.txt", "w");

    FILE *fps = fopen("delayline.txt", "w"); 

    print_array_to_file(fpx, x, N);

    print_array_to_file(fpy, y, N);

    print_array_to_file(fpa, coeffs, P);

    print_array_to_file(fps, s, P);

    fclose(fpx);

    fclose(fpy);

    fclose(fpa);

    fclose(fps);

    return 0;
}