Positive time-frequency distributions via quadratic programming
type: Item
instance of: scholarly article
title: Positive time-frequency distributions via quadratic programming
zbMATH Open document ID: 0988.93057
DOI: 10.1023/A:1008478928534
author: James W. Pitton
published in: Multidimensional Systems and Signal Processing
publication date: 2002-07-14T00:00:00Z
review text: As is known, the Fourier Transform approach does not provide a good solution for nonstationary stochastic signals. A possible approach to such cases is provided by the so-called time-frequency analysis. There exist many ways to achieve it. One of them consists of a bilinear time-frequency representation, which needs an explicit description of a kernel in two variables (it is called distribution). The most widely known distribution is the Wigner distribution, which, however, has some drawbacks. To overcome them, a new object, the positive time-frequency distribution (TFD), is introduced. Simply speaking, a TFD is a time-varying spectrum \(P(t,\omega)\) which obeys the following: a) it is nonnegative; b) its integral with respect to \(\omega\) provides the square of the signal; c) its integral with respect to \(t\) provides the square of the modulus of the Fourier transform of the signal. The paper presents a procedure to obtain the TFD by the use of quadratic programming, i.e. a minimization with respect to an adequate template and two marginal constraints. The paper explains only the main ideas; no example is given.
Mathematics Subject Classification ID: 93C80
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 90C20
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 1236276
zbMATH Keywords: nonstationary stochastic signals
zbMATH Keywords: time-frequency analysis
zbMATH Keywords: bilinear time-frequency representation
zbMATH Keywords: positive time-frequency distribution
zbMATH Keywords: time-varying spectrum
zbMATH Keywords: quadratic programming
reviewed by: Dumitru Stanomir
MaRDI profile type: Publication
full work available at URL: a:1008478928534
OpenAlex ID: W1509349379
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description: scientific article; zbMATH DE number 1236276