On Powers of Gaussian White Noise
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- 30 June 2011
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 57 (11) , 7629-7634
Abstract
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.Keywords
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