Improved discrete definition of quadratic time-frequency distributions

Authors:
John M. O' Toole;Mostefa Mesbah;Boualem Boashash
Affiliations:
University of Queensland, Centre for Clinical Research and Perinatal Research Centre, Royal Brisbane & Women's Hospital, Herston, QLD, Australia;University of Queensland, Centre for Clinical Research and Perinatal Research Centre, Royal Brisbane & Women's Hospital, Herston, QLD, Australia;University of Queensland, Centre for Clinical Research and Perinatal Research Centre, Royal Brisbane & Women's Hospital, Herston, QLD, Australia
Venue:
IEEE Transactions on Signal Processing
Year:
2010

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Abstract

Computation of a time-frequency distribution (TFD) requires a discrete version of the continuous distribution. This discrete TFD (DTFD) should be free from aliasing and conserve all the important mathematical properties of the continuous distribution. Existing DTFD definitions, however, poorly approximate this ideal. One popular definition, the generalized DTFD (GDTFD), is alias free but does not retain all the desirable properties from the continuous distribution. Another definition, the so-called alias-free GDTFD (AF-GDTFD), retains most properties yet is not always alias free. We propose a new DTFD definition, based on the GDTFD, that retains all desirable properties and is always alias free.