Weighted time-frequency and time-scale transforms in reproducing kernel Hilbert spaces

Leon H. Sibul, Lora G. Weiss, Randy K. Young

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Motivated by the time-frequency, time-scale (TF/TS) implementation of a maximum likelihood detector for transient signals in nonstationary Gaussian noise, we define weighted TF/TS transforms using reproducing kernel Hubert space (RKHS) inner products. Inverses of these weighted TF/TS transforms are also given. The particular case of the weight being the inverse noise covariance is presented. The weighted TF/TS transforms turn out to be natural transforms for solving nonstationary detection, estimation, and filtering problems, and have important applications to transient signal estimation in multipath channels with colored nonstationary Gaussian noise.

Original languageEnglish (US)
Pages (from-to)21-22
Number of pages2
JournalIEEE Signal Processing Letters
Volume4
Issue number1
DOIs
StatePublished - Dec 1 1997

Fingerprint

Reproducing Kernel Hilbert Space
Hilbert spaces
Time Scales
Transform
Multipath propagation
Gaussian Noise
Maximum likelihood
Reproducing Kernel Space
Detectors
Multipath Channels
Hubert Space
Scalar, inner or dot product
Maximum Likelihood
Filtering
Detector

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

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Weighted time-frequency and time-scale transforms in reproducing kernel Hilbert spaces. / Sibul, Leon H.; Weiss, Lora G.; Young, Randy K.

In: IEEE Signal Processing Letters, Vol. 4, No. 1, 01.12.1997, p. 21-22.

Research output: Contribution to journalArticle

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