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Article #295Re: Sampled White Gaussian Noise
From: David Kastrup
Date: Thu, 08 Oct 1992 20:00
Date: Thu, 08 Oct 1992 20:00
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1431 bytes
dsimon@atlas.nafb.trw.com writes: >The variance of sampled noise increases with the sampling frequency! >Mathematically it is not so difficult to understand, but I can't >understand it intuitively. Why would the variance change with the >sampling frequency? >Consider a gaussian white noise process with 2-sided PSD N/2. >Then if we take samples of the noise with sampling frequency f, >the variance of each sample is Nf/2. Can anyone expain this intuitively? White noise is uncorrelated, regardless with which frequency you sample. That's the definition. The variance is N, and that's it. The problem lies in your sampling process. If you sample in an integrating manner (integrating over one time slot) instead of taking an instantaneous amplitude, you get a variance depending on the sampling interval. But then you have an implicit sinc(fT) filter in the frequency domain colouring your noise.
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Newsgroups: sci.engr,sci.math Path: arc1-ca.pugleaf.net!sparky!uunet!math.fu-berlin.de!Sirius.dfn.de!Urmel.Informatik.RWTH-Aachen.DE!tabaqui!dak From: dak@tabaqui.informatik.rwth-aachen.de (David Kastrup) Subject: Re: Sampled White Gaussian Noise Message-ID: <dak.718574407@tabaqui> Sender: news@Urmel.Informatik.RWTH-Aachen.DE (Newsfiles Owner) Nntp-Posting-Host: tabaqui Organization: Rechnerbetrieb Informatik / RWTH Aachen References: <1379.2acc1109@atlas.nafb.trw.com> Date: 8 Oct 92 20:00:07 GMT Lines: 19