Wavelet domain implementation of the estimator-correlator and weighted wavelet transforms

Leon H. Sibul, Stefan T. Sidahmed, Teresa L. Dixon, Lora G. Weiss

Research output: Contribution to journalConference article

4 Citations (Scopus)

Abstract

It is well known that the estimator-correlator (EC) is a maximum likelihood detector for random signals in Gaussian noise. In this paper we derive a continuous wavelet domain EC processor for the detection of signals that have propagated over stochastic propagation and scattering channels. The derivation shows that the wavelet transforms that are used for the conditional mean estimator (CME) and for the computation of the detection statistic must be defined by using reproducing kernel Hilbert space (RKHS) inner products rather than ordinary Hilbert space inner products. This fact suggests new weighted wavelet (as well as other time-frequency and time-scale) transforms. These new transforms have many applications to optimum signal processing.

Original languageEnglish (US)
Pages (from-to)1235-1239
Number of pages5
JournalConference Record of the Asilomar Conference on Signals, Systems and Computers
Volume2
StatePublished - Jan 1 1997
EventProceedings of the 1996 30th Asilomar Conference on Signals, Systems & Computers. Part 2 (of 2) - Pacific Grove, CA, USA
Duration: Nov 3 1996Nov 6 1996

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Correlators
Hilbert spaces
Wavelet transforms
Maximum likelihood
Signal processing
Statistics
Scattering
Detectors

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Networks and Communications

Cite this

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Wavelet domain implementation of the estimator-correlator and weighted wavelet transforms. / Sibul, Leon H.; Sidahmed, Stefan T.; Dixon, Teresa L.; Weiss, Lora G.

In: Conference Record of the Asilomar Conference on Signals, Systems and Computers, Vol. 2, 01.01.1997, p. 1235-1239.

Research output: Contribution to journalConference article

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AB - It is well known that the estimator-correlator (EC) is a maximum likelihood detector for random signals in Gaussian noise. In this paper we derive a continuous wavelet domain EC processor for the detection of signals that have propagated over stochastic propagation and scattering channels. The derivation shows that the wavelet transforms that are used for the conditional mean estimator (CME) and for the computation of the detection statistic must be defined by using reproducing kernel Hilbert space (RKHS) inner products rather than ordinary Hilbert space inner products. This fact suggests new weighted wavelet (as well as other time-frequency and time-scale) transforms. These new transforms have many applications to optimum signal processing.

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