White noise and colored noise

During the comparison paper de-noising algorithm, we usually added white Gaussian noise to simulate real-world noise. But in the real world belongs to colored noise.

1: White Noise  

      Refers to the amplitude of Gaussian white noise Gaussian distribution of the signal, and its power spectrum is evenly distributed (a constant), from the engineering point of view, with A noise tends to be regarded as stationary stochastic process rational spectral density, white noise is a random process simple, idealized stochastic process sequence of random variables by a number of unrelated thereof.

2: colored noise:

    White noise over a theoretical sampling, noise is physically difficult to achieve, but the actual measured engineering data is included in colored noise. That so-called colored noise sequences are related to each moment.

3: The difference between the two:

   (1): with a definition, white noise is uncorrelated at different times, the autocorrelation function is an impulse function, colored noise is related.

   (2): actual test can be distinguished by testing the power spectrum, the power spectrum of the white noise in each frequency comparison means average, colored noise will exhibit distinct peaks.

 

N=500;
 
MEAN=0;
 
VAR=1;
 
X=MEAN+VAR*randn(1,N);
 
Y=zeros(1,N);
Y(1)=X(1);
for k=2:N
    Y(k)=X(k)+0.5*X(k-1);
end
 
[Fx fx]=myFFT(X',512);
Zx=1/N*Fx.*conj(Fx);
 
[Fy fy]=myFFT(Y',512);
Zy=1/N*Fy.*conj(Fy);
 
figure
subplot(2,1,1)
plot(X,'-b');
xlabel('k');
ylabel('白噪声')
subplot(2,1,2)
plot(Y,'-b','MarkerFace','g');
xlabel('k');
ylabel('有色噪声')
  
figure
subplot(2,1,1);
plot(fx,Zx);
xlabel('k');
ylabel('白噪声的频谱')

subplot(2,1,2);
plot(fy,Zy);
xlabel('k');
ylabel('有色噪声的频谱')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Run Results: FIG 1 a magnitude spectrum amplitude FIG 2 is not clearly discernible.