On Powers of Gaussian White Noise

Details On Powers of Gaussian White Noise On Powers of Gaussian White Noise

2010-10-14

arxiv.org/abs/1010.2992v1

Computer Science

Information Theory

10 pages

Scientific paper

10.1109/TIT.2011.2158062

Classical Gaussian white noise in communications and signal processing is viewed as the limit of zero mean second order Gaussian processes with a compactly supported flat spectral density as the support goes to infinity. The difficulty of developing a theory to deal with nonlinear transformations of white noise has been to interpret the corresponding limits. In this paper we show that a renormalization and centering of powers of band-limited Gaussian processes is Gaussian white noise and as a consequence, homogeneous polynomials under suitable renormalization remain white noises.

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