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? $\endgroup$ –

2024年7月1日 · From Steven M. Kay's book fundamentals of statistical signal processing, he derives in chapter 3 the CRLB for a single sinusoidal frequency estimation in WGN when the amplitude and phase are known (example 3.5) and the CRLB for a single sinusoidal frequency, amplitude and phase parameters when all three are unknown (example 3.14).

2023年1月11日 · Im working on a Pulsed Doppler Radar What is the way to calculate the SNR (with WGN)? What will be the lowest SNR for detectability? Im using matched-filter(xcorr) to process the signal+noise. My s...

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 ...

2018年1月17日 · 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.

$\begingroup$ @LewisKelsey Why not? $\sigma^2 \delta[k]$ is the auto-correlation sequence of WGN process. And, PSD of WGN process is DTFT of the Auto-correlation sequence which will be $\sigma^2$. DTFTs are $2\pi$-Periodic continuous function of $\omega$. Therefore total power in a period of $-\pi$ to $\pi$ should be $2\pi \sigma^2$. $\endgroup$

$\begingroup$ 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.

2023年4月24日 · 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...