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how to generate white noise of particular frequency in matlab ?

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Aniket
Aniket 2013-4-14
Hello,
I want to generate white noise of particular frequency say 4hz . the covariance is 0.01.
how should i do this in matlab ?

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Youssef Khmou
Youssef Khmou 2013-4-14
hi,
I think you are talking about Colored noise, and bandwidth of 4hz not particular frequency,
White noise contains all the frequencies i.e flat Spectral density, so colored noise can be generated by passing the white noise through low pass filter , here is an example :
x=randn(1000,1); % Additive white Gaussian noise .
% Coefficients
a=1;
b=[1 1];
y=filter(b,a,x);
psd(x);axes=axis, title(' AWGN');
figure,psd(y);axis(axes),title(' Colored Noise');
The colored noise has approximately 0.7 Hz of bandwidth as normalized frequency . so you can adapt the parameters a and b .....
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Aniket
Aniket 2013-4-14
thank you, that i was asking exactly....how should i adjust frequency at 4hz or near to 4hz ?
should i adjust a and b parameters ?
Youssef Khmou
Youssef Khmou 2013-4-14
hi, yes the frequency depends on the parameters a,b or call them the coefficients numerator/denominator of the transfer function of the filter, if you find that difficult, here is the easy way : transform the noise into frequency domain, adjust the frequency and apply the Inverse fourier transform, here is an example :
x=randn(1000,1);
fx=fft(x); % frequency domain .
N=length(fx);
p=0.4/2; % desired bandwidth percentage, /2 because fft is TWO sided !!!
P=round(p*N);
fx(P+1:end)=0;
y=ifft(fx);
psd(x), axes=axis;title(' PSD AWGN');
figure,psd(y), axis(axes), title(' Coloredn');
figure, plot(x), hold on, plot(real(y),'r'), hold off

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Wayne King
Wayne King 2013-4-14
编辑：Wayne King 2013-4-14
White noise cannot be of a particular frequency. White noise by definition is a sequence of uncorrelated random variables. The autocorrelation sequence of a white noise process is the Kronecker delta sequence.
Equivalently, the power spectral density of white noise is constant.
You can easily generate a white noise sequence in MATLAB with a variance of 0.01. You have not specified what distribution the random variables in the white noise sequence should follow (it is not always Gaussian). In this case I'll assume Gaussian. Let N be the length of your sequence.
N = 1000;
noise = sqrt(0.01)*randn(N,1);

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