Time-Frequency Signal Analysis

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Time-Frequency Signal Analysis

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dc.contributor.author Boashash, B
dc.date.accessioned 2012-06-17T15:10:58Z
dc.date.available 2012-06-17T15:10:58Z
dc.date.issued 1991
dc.identifier.citation S. Haykin, editor, “Advances in Spectral Estimation and Array Processing”, Prentice Hall, Vol.1 of 2, Chapter 9, pp. 418 517 en_US
dc.identifier.isbn 0-13-007444-6
dc.identifier.uri http://hdl.handle.net/10576/10832
dc.description This chapter is essentially the 1st comprehensive tutorial on “time-frequency signal analysis” and related topics. This chapter was partly expanded an an update was published in the 1st 3 chapters of 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).
dc.description.abstract This chapter explained the need for defining time-frequency distributions when dealing with nonstationary signals. An attempt was made to provide a comparison between all available TFDs and a clear basis for choice. The criterion of choice is based on one's intuition of how a TFD should perform under some particular condition, for a practical and suitable analysis. The Wigner-Ville distribution has been preferred because it is the closest fit to the ideal time-frequency analysis tool that most signal analysts envisage; it verifies most of the desirable properties and is easily calculated. The notions of instantaneous frequency and time delay of a signal were also reviewed, and it was shown how these parameters are related to time-frequency signal analysis based on the Wigner-Ville distribution. Other properties of the WVD were reviewed and their usefulness for a practical analysis emphasized. The condition of positivity that seems intuitively basic to the concept of a TFD is shown not to be essential in many applications, but it is stressed that what is important is to find a relation between some physical parameters, and some features of the time-frequency distribution, (e.g., energy dissipation and instantaneous frequency [36J, [22]. The limitation of the WVD with regard to cross-terms was addressed. An experienced user of the WVD should be able to interpret correctly these time-frequency representations by discriminating these interferences when they are not too close together. Alternatively, a smoothing procedure will reduce their effect, at the expense of decreased resolution. Potential users of the WD should incorporate the analytic signal (Le., in fact use the WVD) if they want to avoid artifacts and aliasing created by the Wigner distribution (which uses the real signal). Implementation procedures of WVD analysis were shown to be relatively straightforward, in the case of both deterministic and random signals. The potential importance of the method for time-varying filtering of nonstationary signals was demonstrated, and examples were provided. As is the case in standard spectral analYSiS, there is no "best" method in timefrequency signal analysis. The correct approach is to select a TFD that will be optimal for the particular class of signals under consideration. In practice the most useful TFDs, in the author's opinion, are the STFT and the WVD - the STFT because of its negligible cross-terms and the WVD because it gives the least blurred time-frequency representation in the case of monocomponent signals. Other techniques are being currently developed which cater specifically for multicomponent signals. In some specific applications, for example speech, it could be advantageous to use methods such as those developed by Williams and co-workers [20], and Atlas and co-workers [35b]. There are still a number of open questions with regards to time-frequency analysis: positivity, cross-terms, instantaneous frequency, and so on. For further reading it is recommended that a recent tutorial by Mecklenbrauker [95] and a recent review paper by Cohen [32] be consulted.New developments in this field are reported at the annual session on TimeFrequency Signal Analysis organized by SPIE as part of the international conference on advanced signal processing algorithms and architectures, and at the "time-varying spectral analYSis" session of the IEEE International Conference on Acoustics, Speech, and Signal Processing, as well as other conferences. en_US
dc.language.iso en en_US
dc.publisher Prentice Hall en_US
dc.subject spectral characteristic
dc.subject time-frequency distribution
dc.subject quadratic TFDs
dc.subject non-stationary signals
dc.subject instantaneous frequency
dc.subject monocomponent signal
dc.subject multicomponent signal
dc.subject time-frequency analysis
dc.subject time-frequency plane
dc.subject spectral variation
dc.subject t-f energy concentration
dc.subject t-f modeling
dc.subject t-f reconstruction
dc.subject chirp
dc.subject time-varying signal
dc.subject Wigner-Ville Distribution
dc.subject WVD
dc.subject modeling
dc.subject detection
dc.subject recognition
dc.subject time-varying filtering
dc.subject DIF
dc.subject coherence estimation
dc.subject signal internal organization
dc.subject frequency modulation
dc.subject FM
dc.subject t-f laws
dc.subject effective duration
dc.subject effective bandwidth
dc.subject BT product
dc.subject t-f representation
dc.subject asymptotic signal
dc.subject time-bandwidth
dc.subject t-f plane
dc.subject t-f elementary cell
dc.subject t-f characteristic
dc.subject t-f spread
dc.subject t-f formulation
dc.subject STFT
dc.subject short-time Fourier transform
dc.subject sonogram
dc.subject Ambiguity function
dc.subject energy spectral density
dc.subject uncertainty principle
dc.subject spectrum gradient
dc.subject Vibroseis
dc.subject stationary phase
dc.subject discrete-time TFD
dc.subject butterfly functions
dc.subject artifacts
dc.subject artefacts
dc.subject central finite difference
dc.subject t-f support
dc.subject WVD invertibility
dc.subject average frequency
dc.subject DWVD
dc.subject discrete-time analytic signal
dc.subject discrete-time Hilbert transform
dc.subject DIF
dc.subject t-f filtering
dc.subject instantaneous bandwidth
dc.subject IF spread
dc.subject evolutive spectrum
dc.subject power spectral density
dc.subject t-f plan
dc.subject local ergodicity
dc.subject signal segmentation
dc.subject t-f coherence
dc.subject WVD synthesis
dc.subject valid WVD
dc.subject signal enhancement
dc.subject signal separation
dc.subject t-f feature
dc.subject detection statistic
dc.subject Moyal’s formula
dc.subject transient detection
dc.subject ECG
dc.subject machine noise
dc.subject energy dissipation
dc.title Time-Frequency Signal Analysis en_US
dc.type Book chapter en_US

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