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

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

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

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

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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 language	English (US)
Pages (from-to)	1235-1239
Number of pages	5
Journal	Conference Record of the Asilomar Conference on Signals, Systems and Computers
Volume	2
State	Published - Jan 1 1997
Event	Proceedings of the 1996 30th Asilomar Conference on Signals, Systems & Computers. Part 2 (of 2) - Pacific Grove, CA, USA Duration: Nov 3 1996 → Nov 6 1996

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All Science Journal Classification (ASJC) codes

Signal Processing
Computer Networks and Communications

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Sibul, L. H., Sidahmed, S. T., Dixon, T. L., & Weiss, L. G. (1997). Wavelet domain implementation of the estimator-correlator and weighted wavelet transforms. Conference Record of the Asilomar Conference on Signals, Systems and Computers, 2, 1235-1239.

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title = "Wavelet domain implementation of the estimator-correlator and weighted wavelet transforms",

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.",

author = "Sibul, {Leon H.} and Sidahmed, {Stefan T.} and Dixon, {Teresa L.} and Weiss, {Lora G.}",

year = "1997",

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language = "English (US)",

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note = "Proceedings of the 1996 30th Asilomar Conference on Signals, Systems & Computers. Part 2 (of 2) ; Conference date: 03-11-1996 Through 06-11-1996",

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TY - JOUR

T1 - Wavelet domain implementation of the estimator-correlator and weighted wavelet transforms

AU - Sibul, Leon H.

AU - Sidahmed, Stefan T.

AU - Dixon, Teresa L.

AU - Weiss, Lora G.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - 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.

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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M3 - Conference article

AN - SCOPUS:0030647524

VL - 2

SP - 1235

EP - 1239

JO - Conference Record of the Asilomar Conference on Signals, Systems and Computers

JF - Conference Record of the Asilomar Conference on Signals, Systems and Computers

SN - 1058-6393

T2 - Proceedings of the 1996 30th Asilomar Conference on Signals, Systems & Computers. Part 2 (of 2)

Y2 - 3 November 1996 through 6 November 1996

ER -

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

Abstract

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All Science Journal Classification (ASJC) codes

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