How to create a complex Gaussian random noise with a specific covariance matrix
I am trying to generate a complex Gaussian white noise, with zero mean and the covariance matrix of them is going to be a specific matrix which is assumed to be given.
Assume i to be a point on the grid of x axis, where there are N points on the axis. The problem is to generate a complex valued random noise at each point (let's call the random value at the point i as $y_i$), which obeys Gaussian distribution and has a covariance matrix of,
$E((y_i)(y_j^*)) = c_{ij}$
where $c_{ij}$ is a given diagonal NxN matrix. * is complex conjugate, E represents the expectation value.
I am trying to generate this on Python.
Topic noise numpy gaussian python
Category Data Science