# [R] noise poser spectral density

From: DIM PATRIDGE <dimpatridge_at_yahoo.co.uk>
Date: Sat 04 Jun 2005 - 04:16:48 EST

Dear Signal Processing Expert,
I would like to generate a random stationary signal of gaussian probability density function to simulate narrow band noise at the output of an IF amplifier. I know the receiver's system temperature (Ts) and IF bandwidth (B) therefore I assume that my narrow band noise mean power equals KTsB watts and therefore the power spectral density No=KTs per Hz. Do you know any relationship between No and sigma^2 so I can simulate the stationary random signal in matlab? Theory says that for white noise No/2=sigma^2 but this formula I believe is only valid for white broadband noise. I will appreciate your opinion.
Regards
Dim Patridge

I know there are some time series experts on this list, and I am hoping one of you might help me with this problem. I am trying to understand the relationship between No (noise power spectral density) and Gaussian white noise sigma^2.

I want to check numerically the theoretical relationship (from Selin,1965) No = sigma^2/(2*W) = sigma^2 * delta t, where No is power spectral density
delta t is sampling interval in sec = 1/(2*W) W is the bandwidth: the power spectral density (psd) is flat (equal to No) for freqs between -W and W Hz

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