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 andItalic text frequency domain, a key difference from the traditional signal representations that are either time domain representations orItalic text 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 analysis but also for processing.

Historical 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 (re-spelled "Boualem Boashash" after his move to Australia); in the Netherlands, the development took place in Philips and was led by Claasen and Mecklenbrauker. 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 the estimation of absorption in vertical seismic prospecting for the purpose of a more accurate determination of oil reservoirs contours; Boualem Boashash was a student of Bernard Escudie but doing his PhD in industry (ie elf-aquitaine); and Bernard Escudie had another student, Patrick Flandrin who utilized the results from elf-aquitaine to study the structure of interference terms in TFDS . 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 under the leadership of Boualem Boashash 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 under the chairmanship of Boualem Boashash. This was preceded by the SPIE special session on time-frequency signal analysis that was organised and chaired by Boualem Boashash between 1985 and 1995. During this time, Leon Cohen became aware of these developments and he realized that the formulations used to define TFDs were the same as the ones he used in Quantum Mechanics. He then joined the effort of the Australian team and went on to publish 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 , the need to use the analytic signal in the formulation of the Wigner-Ville Distribution and other TFDs, and the importance of progressing the design of efficient algorithms. To further this effort, Boualem Boashash decided to set up ISSPA to provide another focus for the dissimination of the research results in TFSP (link to isspa87); the 2nd ISSPA in 1990 included the special international conference on TFSA. It is on the basis of these developments that at this time an application was successfully made to hold ICASSP in Australia for which Boualem Boashash was technical chairman. From the 1990s, more researchers became involved in the development of TFSP and they are too many to be listed here, and a short selection could risk being subjective. Several books were published in this field from that point, the most comprehensive being .

~ 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. ~ ~

The following headings link to some other relevant articles

Time series

Signal processing Frequency domain Time–frequency representation

Bilinear time-frequency distribution

Transformation between distributions in time-frequency analysis Time–frequency analysis

Instantaneous phase

Analytic signal

Wavelet

Fourier transform

Wigner distribution function

Harmonic wavelet transform

S transform

Coherence (signal processing)