In the description of any Beamforming Technique for microphone array signal processing there is a usage of the co-relation matrix.
What is the use of calculating such a co-relation matrix in such algorithms?
In the description of any Beamforming Technique for microphone array signal processing there is a usage of the co-relation matrix.
What is the use of calculating such a co-relation matrix in such algorithms?
Sometimes you calculate it or sometimes you know it by the assumptions of a particular problem. Most typically you estimate it $$ R=\frac{1}{N} \sum x_k x_k^H $$ where $x_k$ is a vector of outputs at time $k$. This is the “narrow band” case, at a single frequency. The inverse of $R$ is often more important.
$R$ is sometimes called the cross spectral density matrix CSDM and sometimes the cross matrix
The theoretical root of importance $R$ is that it represents the covariance of a Gaussian probability density . $$ w^H R w $$ Is the expected output power the array given $w$ which is the weight vector, A large number of algorithms are based on power and power is related to SNR,
If $R$ is estimated or known , you can calculate the weights of the MVDR beam former. Which is one application.
Another is that you can spatially whiten the output of sensors with the square root of $R$
The eigenvalues of $R$ are important in subspace techniques like MUSIC .
There are more applications but the common assumption is that your data is Gaussian or similar to Gaussian