I have the power spectral density function of a stochastic phenomenon.
- how can I generate a signal (time series) representing the randomness of this event over time?
- How can I draw the probability distribution and commutative distribution functions from the given PSD in order to take N samples using the basic monte Carlo method?
The answer of (2) can be used to model the uncertainty of an event to use in Stochastic programming. We should get N samples, with an equal probability of 1/N.
The answer to (1) can be used to evaluate the given results of the stochastic programming by out-of-sample analysis.
Since I am not so familiar with Signal Processing notations, it would better to have the answer in form of an algorithm or Matlab/Python code, if possible.