Hi Yara,
I understand that you want to generate colored noise samples from the noise covariance matrix and the SNR (Signal-to-noise ratio).
You can follow these steps in MATLAB:
- Calculate the noise power "Pn" based on the SNR and the source signal power "Ps".
- Define the noise covariance matrix "Q" using the given formula for Qm,l.
- Generate samples from a multivariate normal distribution using the defined matrix "Q".
Here is a sample code to generate the noise sample:
N = 9;
Pn = Ps / SNR;
Q = zeros(N, N);
for m = 1:N
for l = 1:N
Q(m, l) = Pn * exp(-0.5 * (m - l)^2);
end
end
% Assuming that you want to generate a single sample vector
noiseSample = mvnrnd(zeros(1, N), Q);
% If you want to generate multiple samples, say 1000 samples, you can use:
% noiseSamples = mvnrnd(zeros(1, N), Q, 1000);
disp(noiseSample);
When you generate a sample from a multivariate normal distribution with this covariance matrix using the "mvnrnd" function, you get a vector of noise samples that are correlated according to the structure defined by "Q". This is what makes the noise "colored" because the values are not independent.
Note that if the "SNR" is given in decibels (dB), you will need to convert it to linear scale using SNR_linear = 10^(SNR_db/10) before using it in the calculation of "Pn".
You can refer the following documentation to read more about "mvnrnd":
Hope this helps!
