A Novel Approach for the Wigner Distribution Formulation of the Optimum Detection Problem for a Discrete-Time Chirp Signal


  1. Thayaparan, T.
  2. Yasotharan, A.
Corporate Authors
Defence Research Establishment Ottawa, Ottawa ONT (CAN)
The Wigner distribution is a signal transformation which has its origin in quantum mechanics. It possesses some important properties which make it very attractive for time-frequency signal analysis. The Wigner distribution was originally defined for continuous-time signals. A discrete-time version of it was proposed recently. Unfortunately, this discrete-time Wigner distribution suffers from aliasing effects, which prevent several of the properties of the continuous-time Wigner distribution from carrying over straightforwardly. In this report, a discrete-time Wigner distribution which does not suffer from aliasing is introduced. It is essentially an augmentation of the previous version incorporating new information about the signal not contained in the previous version. A variety of methods have been proposed for the detection of a signal, with unknown signal parameters, in a noisy environment. In this report, the noise statistics are incorporated to reveal that certain processing of the Wigner distribution signal representation can lead to an optimal, and often easy to compute, detection scheme. For the special case of discrete-time chirp signals in complex white Gaussian noise, it is shown that the optimal detector is equivalent to integrating the Wigner distribution along the line of instantaneous frequency. TRUNCATED

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Time-frequency analysis;Discrete-time signal;Wigner distribution;GLRT (Generalized Likelihood Ratio Test);Fourier transform;Radon transform;Instantaneous frequency;High-frequency radar;Doppler processing;Accelerating targets;Doppler smearing;Generalized velocity;Generalized acceleration
Report Number
DREO-TM-2001-141 — Technical Memorandum
Date of publication
01 Nov 2001
Number of Pages
Hardcopy;Document Image stored on Optical Disk

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