Weighted time-frequency and time-scale transforms for non-stationary signal detection

Lora G. Weiss, Leon H. Sibul

Research output: Contribution to journalConference article

Abstract

Maximum likelihood detectors of narrowband, non-stationary random echos in Gaussian noise can be efficiently implemented in the time-frequency domain. When the transmitted signals have large time-bandwidth products, the natural implementation of estimators and detectors is the time-scale or wavelet transform domain implementation. This paper extends the wavelet transform implementations to include weighted time-frequency or time-scale (TF/TS) transforms. We define weighted TF/TS transforms using Reproducing Kernel Hilbert 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. We show how weighted transforms are used in the estimator-correlator detection statistic for complex scattering environments in conjunction with cascaded scattering functions so that the resulting detection statistic is much more robust. The weighted TF/TS transform turns out to be a natural transform for solving nonstationary detection, estimation, and filtering problems and has important applications to transient signal estimation in multipath channels with colored non-stationary Gaussian noise.

Original languageEnglish (US)
Pages (from-to)368-377
Number of pages10
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume3169
DOIs
StatePublished - Dec 1 1997
EventWavelet Applications in Signal and Image Processing V - San Diego, CA, United States
Duration: Jul 30 1997Jul 30 1997

Fingerprint

Non-stationary Signal
Signal Detection
signal detection
Signal detection
Wavelet transforms
Time Scales
Statistics
Scattering
Transform
Detectors
Multipath propagation
Correlators
Hilbert spaces
Maximum likelihood
Gaussian Noise
Bandwidth
Wavelet Transform
Statistic
Detector
Multipath Channels

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

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abstract = "Maximum likelihood detectors of narrowband, non-stationary random echos in Gaussian noise can be efficiently implemented in the time-frequency domain. When the transmitted signals have large time-bandwidth products, the natural implementation of estimators and detectors is the time-scale or wavelet transform domain implementation. This paper extends the wavelet transform implementations to include weighted time-frequency or time-scale (TF/TS) transforms. We define weighted TF/TS transforms using Reproducing Kernel Hilbert 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. We show how weighted transforms are used in the estimator-correlator detection statistic for complex scattering environments in conjunction with cascaded scattering functions so that the resulting detection statistic is much more robust. The weighted TF/TS transform turns out to be a natural transform for solving nonstationary detection, estimation, and filtering problems and has important applications to transient signal estimation in multipath channels with colored non-stationary Gaussian noise.",
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Weighted time-frequency and time-scale transforms for non-stationary signal detection. / Weiss, Lora G.; Sibul, Leon H.

In: Proceedings of SPIE - The International Society for Optical Engineering, Vol. 3169, 01.12.1997, p. 368-377.

Research output: Contribution to journalConference article

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AU - Sibul, Leon H.

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AB - Maximum likelihood detectors of narrowband, non-stationary random echos in Gaussian noise can be efficiently implemented in the time-frequency domain. When the transmitted signals have large time-bandwidth products, the natural implementation of estimators and detectors is the time-scale or wavelet transform domain implementation. This paper extends the wavelet transform implementations to include weighted time-frequency or time-scale (TF/TS) transforms. We define weighted TF/TS transforms using Reproducing Kernel Hilbert 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. We show how weighted transforms are used in the estimator-correlator detection statistic for complex scattering environments in conjunction with cascaded scattering functions so that the resulting detection statistic is much more robust. The weighted TF/TS transform turns out to be a natural transform for solving nonstationary detection, estimation, and filtering problems and has important applications to transient signal estimation in multipath channels with colored non-stationary Gaussian noise.

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