May 18, 2023 · $\begingroup$ Good answer except I question the 2nd sentence: my thinking was that we can indeed simulate SAMPLES of a mythical continuous time WGN process and it would be mathematically accurate (without the requirement that it be bandlimited). What would end up being a CT WGN with PSD =0 would all alias to a DT WGN with finite non-zero PSD.

wgn() is specifically meant to create a white noise with a predefined power levels while randn() is meant to generate normally distributed random numbers WITHOUT specifying the power. You will have to scale the values generated from randn() to meet the desired noise power level.

But you say " One should not, however, infer that the random variables in the WGN process are themselves Gaussian random variables". I did not fully understand this. If the random variables aren't Gaussian (and this seems reasonable to me since they have infinite variance), why is the process named Gaussian? $\endgroup$ –

Jan 17, 2018 · DC level in signal processing refers to the average or the mean value of a signal. So a zero-mean signal will have an average value of zero over its domain of definition.

Since the input process has zero mean, so does the output process have zero mean, that is, all the random variables constituting the process have zero mean. For the case of WGN, the filter output is a strictly stationary Gaussian process, meaning that all the random variables are Gaussian random variables. As a special case of all this, if the ...

$\begingroup$ good answer with lots of details, but fails to concisely answer the basic question -- OP: Ignore your intuition; adding WGN on the real axis with WGN on the imaginary axis results in complex WGN.

Sep 1, 2023 · My guess is that I can synthesize WGN using MATLAB's wgn function, and then filter it. However, I'm not sure how to create the filter. However, I'm not sure how to create the filter. Additionally, my signal is single ended so I guess I should add some offset to account for it.

Jul 25, 2013 · The "information content" is related to the number of samples. The length of the FFT merely interpolates the spectral frequency curve represented by the number of samples.

Apr 24, 2023 · Follow Up with Intuition Related to Zero PSD for WGN With Finite Variance. MBaz and RBJ have rightfully questioned my reasoning of a zero power spectral density in the comments, suggesting that the variance would increase for a constant power spectral density as the bandwidth increases.

I would like to synthesize a first order Gauss-Markov process from a white Gaussian noise. I know from signal processing theory that it could be realized using a noise shaping filter designed prope...