Hilbert transformer and time delay: statistical comparison in the presence of Gaussian noise

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Hilbert transformer and time delay: statistical comparison in the presence of Gaussian noise

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Title: Hilbert transformer and time delay: statistical comparison in the presence of Gaussian noise
Author: Hussain, Z.M; Boashash, Boualem
Abstract: We have shown that in the presence of independent and identically distributed (i.i.d.) additive Gaussian noise, the performance of a time delay as a phase shifter, which produces a signal-dependent phase shift, is comparable with the performance of a Hilbert transformer which produces a signal-independent 90° phase shift, especially for high signal-to-noise ratios (SNRs) and the proper choice of the delay. Sinusoidal signals are considered. It is shown that the time-delay phase process in Gaussian noise can be approximated by the noise-free phase plus a non-Gaussian phase noise. As the SNR increases, the expected value of the time-delay phase estimator approaches the true value of the phase, and its variance substantially decreases and converges to the Cramer-Rao bound for all ranges of the effective parameters: the phase shift, the deterministic phase, and SNR. A symmetric transformation of the phase probability density function (PDF) that improves the performance of the time delay in Gaussian noise is also proposed.
Description: A time-delay can be used instead of, or, to implement the Hilbert Transform for quadrature phase shifting.
URI: http://hdl.handle.net/10576/10674
Date: 2002-03

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