Application of the envelope-phase representation in some non-linear noise problems†
01 Mar 1968-International Journal of Electronics (Taylor & Francis Group)-Vol. 24, Iss: 3, pp 201-209
TL;DR: It is shown here that this approach is equally good for the more general problem of evaluating the output power‡ series of a non-linearity of either single-valued or double-valued type.
Abstract: The paper discusses an extension of some of the earlier works of the author and his student on a procedure for evaluating the transmission properties of gaussian signals through non-linear devices. It is based on the application of the envelope-phase representation of such signals and subsequent application of the Fourier series expansion of the instantaneous output of the non-linearity. The earlier investigations were concerned mainly with the evaluation of the input-output cross-power‡ terms. It is shown here that this approach is equally good for the more general problem of evaluating the output power‡ series of a non-linearity of either single-valued or double-valued type. An application of those computations in the field of nonlinear filtering is discussed.
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807 citations
TL;DR: Application is made to the interesting special cases of conventional cross-correlation and autocorrelation functions, and Bussgang's theorem is easily proved.
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TL;DR: By using the pre-envelope, the envelope of the output of a linear filter is easily calculated, and this is used to compute the first probability density for the envelopes of an arbitrary linear filter when the input is an arbitrary signal plus Gaussian noise.
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