User:Burhem/Time-frequency signal processing
Introduction to TFSP
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 of TFSP
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 B. Bouachache[1] (re-spelled "B. 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 B. 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. In paralled, an SPIE special session on time-frequency signal analysis 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 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 /refer/baraniuk and jones/ and new applications to detection, classification and filtering/refer/sayed/. 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 TFSP relevant 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
Signal Processig Concepts and Methods
Time series is the terminology used in the field of Mathematics to design a signal.
Signal processing is the broader field of which Time-Frequency Signal Processing is a sub-field.
Frequency domain is particular axis of the time-frequency domain.
Time-Frequency concepts and Methods
Time–frequency representation is concerned with defining the best mathematical formulation to represent signals in a joint time-frequency domain.
Wigner distribution function or Wigner-Ville Distribution is the core time-frequency representation used to represent signals in a joint time-frequency domain.
Bilinear time-frequency distribution is a class of TFDS that have specific properties that make them suitable to represent signals in a joint time-frequency domain. The Wigner-Ville Distribution is a particular member of this class.
Transformation between distributions in time-frequency analysis is a useful way to move from one time-frequency representation to another way without having to recompute the whole TFD.
Time–frequency analysis refers to the use of TFDs to analyse a signal and find its characteristics in a joint time-frequency domain.
Instantaneous Frequency(IF) is a function of time which describes the variations of the signal spectral contents with time.Instantaneous Frequency is one of the key concepts of TFSP as the IF establishes a practical and conceptual link between the time domain and the frequency domain.
Frequency Modulation(FM) is an example of practical use of the IF in Telecommunications for Radio transmission where the FM is given by the IF of the signal.
Instantaneous Phase is the integral of the signal instantaneous irequency.
Analytic signal is a complex signal formed by adding an imaginary part to the real signal, where the imaginary part is the Hilbert Transform of the real part. This key concept defines the complex signal z(t) associated with the real signal s(t). Its use in the formulation of the WD results in the WVD which leads to the practical use of the WVD for time-frequency representation of signals.
Time-Scale concepts and Methods
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