粉红噪声是一种无规则的噪声，具有连续的噪声谱，其功率与频率呈反比，频率成分比白噪声多，在固定的倍频程带宽内，声能量相同的。如低频125~250Hz带宽与高频2K~4K带宽内能量是相同的。

白噪声属于全频噪声，主要用来测量电声设备，粉红噪声是根据人耳的听觉特性与习惯
设计出的测量噪声，主要用来模拟人的听觉，测量厅堂的声学特性

function out = create_pink_noise(Fs, Sec, Amp)

% Creates a pink noise signal and saves it as a wav file
%
% Usage: create_noise(Fs, Sec, Amp);
%
%        Fs is the desired sampling rate
%        Sec is the duration of the signal in seconds
%        Amp is the amplitude in dB of the signal (0dB to -144dB)
%
% Author: sparafucile17 06/14/02

%error trapping
if((Amp > 0) || (Amp < -144))
    error('Amplitude is not within the range of 0dB to -144dB');
end

%Create Whitenoise
white_noise = randn((Fs*Sec)+1,1);

%Apply weighted sum of first order filters to approximate a -10dB/decade
%filter.  This is Paul Kellet's "refined" method (a.k.a instrumentation
%grade)  It is accurate to within +/-0.05dB above 9.2Hz
b=zeros(7,1);
for i=1:((Fs*Sec)+1)
    b(1) = 0.99886 * b(1) + white_noise(i) * 0.0555179;
    b(2) = 0.99332 * b(2) + white_noise(i) * 0.0750759;
    b(3) = 0.96900 * b(3) + white_noise(i) * 0.1538520;
    b(4) = 0.86650 * b(4) + white_noise(i) * 0.3104856;
    b(5) = 0.55000 * b(5) + white_noise(i) * 0.5329522;
    b(6) = -0.7616 * b(6) - white_noise(i) * 0.0168980;
    pink_noise(i) = b(1) + b(2) + b(3) + b(4) + b(5) + b(6) + b(7) + white_noise(i) * 0.5362;
    b(7) = white_noise(i) * 0.115926; 
end

%Normalize to +/- 1
if(abs(min(pink_noise)) > max(pink_noise))  
    pink_noise = pink_noise / abs(min(pink_noise));
else
    pink_noise = pink_noise / max(pink_noise);
end

%Normalize to prevent positive saturation (We can't represent +1.0)
pink_noise = pink_noise /abs(((2^31)-1)/(2^31));

%Scale signal to match desired level
pink_noise = pink_noise * 10^(Amp/20);

%Output noise signal
out = pink_noise(1:end-1);

这里使用了两种 Paul Kellet 的滤波方法 降低误差，滤波系数是

Here are some new lower-order pink noise filter coefficients.

These have approximately equiripple error in decibels from 20hz to 20khz at a 44.1khz
sampling rate.

1st order, ~ +/- 3 dB error (not recommended!)
num = [0.05338071119116  -0.03752455712906]
den = [1.00000000000000  -0.97712493947102]

2nd order, ~ +/- 0.9 dB error
num = [ 0.04957526213389  -0.06305581334498   0.01483220320740 ]
den = [ 1.00000000000000  -1.80116083982126   0.80257737639225 ]

最上面的使用更高阶次的实现滤波相关 减小误差