如何根据噪声的相关性得出噪声是否为白色的结论？

Question

我的问题是：通过使用自相关，如何推断该噪声是否为白色？ 我生成了均匀噪声和高斯噪声，然后使用xcorr指令进行自动相关，如下所示：

%=======================================
% Generate Random Signals
%=======================================
% Define the distribution that you'd like to get
mu    = 2.5; % Median
sigma = 2.0; % Variance
% You can any size matrix of values
sz = [10000 1]; % size of samples
%-----------------------------------------
% Generating Gaussian Noise
Gaussian_Noise = (randn(sz) * sigma) + mu;
%---------------------------------
%  | mean(value)   |  std(value) |
%  |   2.4696      |   1.9939    |
%  -------------------------------
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% Generating uniform Distributed Noise
UniForm_Noise = (rand(sz) * sigma) + mu;
%----------------------------------------
% Plotting The Gaussian Noise
figure('Name','Noise with Histograms','NumberTitle','off');
subplot(231);
plot(Gaussian_Noise)
title('Gaussian Noise')
subplot(232);
histogram(Gaussian_Noise,64); % 64 is number of bins
title('Gaussian Histogram')
%----------------------------------------------------
subplot(233);
plot(xcorr(Gaussian_Noise, 300))
%autocorr(Gaussian_Noise,'NumLags',1000);
% corr1 = autocorr(Gaussian_Noise);
% F1 = fft2(corr1);
% FSh1 = fftshift(F1);
% imshow(abs(FSh1))
title('Gaussian Noise Auto Correlation')
%----------------------------------------------------
subplot(234);
plot(UniForm_Noise)
title('UniForm Noise')
subplot(235);
histogram(UniForm_Noise,64); % 64 is number of bins
title('UniForm Noise Histogram')
%----------------------------------------------------
subplot(236);
plot(xcorr(Uniform_Noise, 300))
%autocorr(UniForm_Noise,'NumLags',1000)
title('UniForm Noise Auto Correlation')
%---------------------------------------

Answer 1

白色噪声是由所有频率组成的，就像白光又由所有颜色组成一样。如果结果看起来像中心的狄拉克脉冲，我们可以从结果的自相关推断出噪声是白色的。