Efficient algorithms for discrete time-frequency distributions

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Efficient algorithms for discrete time-frequency distributions

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Title: Efficient algorithms for discrete time-frequency distributions
Author: O'Toole, J; Mesbah, M; Boashash, B
Abstract: Time­-frequency distributions (TFDs) are computationally costly to compute. This paper presents algorithms to reduce this computational load. Before we can compute the TFDs, however, we must define a discrete version of the TFD. Defining a discrete TFD (DTFD) is not a straightforward process---for example, a popular DTFD definition does not satisfy all desirable mathematical properties that are inherent to the continuous TFD. In this paper, we define a new DTFD definition, the DTFD-C. This definition is closely related to another DTFD definition which we recently proposed, the DTFD-B. The DTFD-B and DTFD-C satisfy all desirable properties. We provide algorithms for both these definitions and show that the DTFD-C requires only 50% of the computational load required to compute the DTFD-B.
Description: This paper shows that a new discrete time version of TFDs the DTFD-C, has the clear advantage over the other definitions as it provides the signal analyst with a high performance tool, by retaining all useful properties, at a low computational cost. (Additional details can be found in the comprehensive book on Time-Frequency Signal Analysis and Processing (see http://www.elsevier.com/locate/isbn/0080443354). In addition, the most recent upgrade of the original software package that calculates Time-Frequency Distributions and Instantaneous Frequency estimators can be downloaded from the web site: www.time-frequency.net. This was the first software developed in the field, and it was first released publicly in 1987 at the 1st ISSPA conference held in Brisbane, Australia, and then continuously updated).
URI: http://hdl.handle.net/10576/10804
Date: 2008

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