User:Burhem/Time-frequency signal processing
Introduction
The field of "time-frequency signal processing" (TFSP) is a sub-field of "signal processing" that has grown enormously since the 1980s; it is concerned with the representation, analysis and processing of signals whose spectral characteristics are time-varying. TFSP represents signals (or time-series) in a joint time and frequency domain, a key difference from the traditional signal representations that are either time domain representations or a frequency domain representation. Such a representation uses Time-Frequency Distributions that are mathematical formulations for showing the distribution of signal energy in the time-frequency plane. Such a TFSP approach allows us to take into account information not accessible through trational signal processing methods so that this new information allows a more accurate representation, analysis and processing; all traditional applications of signal processing would benefit from this approach. In terms of terminology, TFSP is now more appropriate than TFSA as TFDS are now used not only for signal analysis in the time-frequency (t,f) domain but also for signal processing in the (t,f) domain. Such processing includes (t,f) filtering, parameter estimation, signal detection and classification, feature extraction and many others.
Background
A major historical development occurred in the late 1970s and early 80s simulaneously and independently in France and the Netherlands, facilitated by new progress in computing, that led to what are known as the earliest applications of TFSP to real-life problems. In France, this development took place in elf-aquitaine (now Total) and was led by Boualem Bouachache[1] (re-spelled "Boualem Boashash" after he settled in Australia); in the Netherlands, the development took place in Philips and was led by Claasen and Mecklenbrauker[2]. Independently of each other, both Boualem Boashash and Claasen and Mecklenbrauker applied TFSP to a practical application relevant to the company employing them; in France, the application was to use the Wigner-Ville Distribution and the instantaneous frequency for the estimation of absorption in vertical seismic prospecting for the purpose of a more accurate determination of oil reservoirs contours. In the Netherlands, the application related to the design of loudspeakers. Both teams independently designed an algorithm for implementing the Wigner Distribution and applied it to their engineering problem. In 1984, a major effort started to take place in Australia that focussed on making further progress in applying the TFSP concepts and methods to new applications. For this purpose, the first TFSA package was set-up in Fortran, then C and then Matlab in the 1980s, and the first conference on Time-Frequency Signal Analysis took place in 1990 in Brisbane Australia. This was preceded by the SPIE special session on time-frequency signal analysis that was organised by the same team leader between 1985 and 1995. During this time, other auhors became aware of these developments and realized that the formulations used to define TFDs were the same as the ones he used in Quantum Mechanics. They then joined the effort of the Australian team and went on to publish a review of the results (proc. of ieee) and book tfsa, facilitated by the TFSA software that was then available from the Australian team at the University of Queensland. The Australian team emphasized a holistic approach that included developments of the theory, its implementation and application to real-life applications with special focus on the interpretation and estimation of the concept of instantaneous frequency [3], the need to use the analytic signal in the formulation of the Wigner-Ville Distribution[4] and other TFDs, and the importance of progressing the design of efficient algorithms[5].
From "Time-Frequency Signal Analysis to "Time-Frequency Signal Processing"
From the 1990s, more researchers became involved in the development of TFSP; these efforts led to new advances in designing TFSP methods with greater accuracy, with data dependent formulations and new applications to detection, classification and filtering. These developments allowed to not just analyze but also process signals in a joint time-frequency domain, allowing the possibility of more real-life applications as reported in the most comprehensive treatment of these questions found in [6].
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Commented links to other time-frequency articles
We list below the links to existing articles that provide additional information to complement this article, and provide a comment for each link so as to clarify the context of these articles and the relevance to this material. To make it easier to the reader, these links are ordered and grouped according to technical topics. ~ ~
The following headings link to some other relevant articles
Time series is the mathematical terminology for a signal.
Bilinear time-frequency distribution
Transformation between distributions in time-frequency analysis
Example of Application of TFSP
references
- ^ B. Bouachache, "Representation temps-frequence," Soc. Nat. ELF Aquitaine, Pau, France, Publ. Recherches, no. 373-378, 1978
- ^ T. A. C. M. Classen and W. F. G. Mecklenbrauker, “The Wigner distributiona tool for time-frequency signal analysis; Part I,” Philips J. Res., vol. 35, pp. 217–250, 1980.
- ^ B. Boashash, "Estimating and Interpreting the Instantaneous Frequency of a Signal-Part I: Fundamentals", Proceedings of the IEEE, Vol. 80, No. 4, pp. 519-538, April 1992
- ^ B. Boashash, "Note on the Use of the Wigner Distribution for Time Frequency Signal Analysis", IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 36, No. 9, pp. 1518–1521, Sept. 1988
- ^ B. Boashash and P. Black, "An Efficient Real-Time Implementation of the Wigner-Ville Distribution", IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 35, No. 11, pp. 1611-1618, November 1987.
- ^ B. Boashash, editor, “Time-Frequency Signal Analysis and Processing – A Comprehensive Reference”, Elsevier Science, Oxford, 2003; ISBN 0080443354