Heuristic Formulation of Time-Frequency Distributions

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Heuristic Formulation of Time-Frequency Distributions

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dc.contributor.author Boashash, B
dc.date.accessioned 2012-02-21T16:17:23Z
dc.date.available 2012-02-21T16:17:23Z
dc.date.issued 2003
dc.identifier.citation Time-Frequency Signal Analysis & Processing: A Comprehensive Reference, Elsevier Science, Oxford, 2003, Chapter 2, pages 29-58 en_US
dc.identifier.isbn 0080443354
dc.identifier.isbn 9780080443355
dc.identifier.uri http://hdl.handle.net/10576/10788
dc.description This manuscript constructs a number of quadratic TFDs (time-frequency methods) from basic principles; this includes the most popular time-frequency methods including the Wigner-Ville Distribution and the Spectrogram. (Additional details can be found in the other 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). en_US
dc.description.abstract Having established the basic signal formulations in the first chapter, we now turn to the problem of representing signals in a joint time-frequency domain. Given an analytic signal z(t) obtained from a real signal s(t), we seek to construct a time-frequency distribution z(t, f) to represent precisely the energy, temporal and spectral characteristics of the signal. We choose the symbol z in the expectation that the TFD will represent an “energy density of z” in the (t, f) plane. We would also like the constant-t cross-section of z(t, f) to be some sort of “instantaneous spectrum” at time t. In this chapter we examine a variety of ad hoc approaches to the problem, namely the Wigner-Ville distribution (Section 2.1), a time-varying power spectral density called the Wigner-Ville Spectrum (2.2), localized forms of the Fourier Transform (2.3), filter banks (2.4), Page’s instantaneous power spectrum (2.5), and related energy densities (2.6). Finally (in Section 2.7), we show how all these distributions are related to the first-mentioned Wigner-Ville distribution, thus setting the scene for the more systematic treatment in the next chapter. The various distributions are illustrated using a linear FM asymptotic signal. The linear FM signal [Eq. (1.1.5)] is regarded as the most basic test signal for TFDs because it is the simplest example of a signal whose frequency content varies with time. It is clearly monocomponent, and is asymptotic if its BT product is large. The minimum requirement for a useful TFD is that it clearly shows the IF law of an asymptotic linear FM signal, giving a reasonable concentration of energy about the IF law (which, for an asymptotic signal, is equivalent to the TD law). en_US
dc.language.iso en en_US
dc.publisher Elsevier en_US
dc.subject time-frequency distribution construction en_US
dc.subject instantaneous spectrum en_US
dc.subject time-varying power spectral density en_US
dc.subject Wigner-Ville Spectrum en_US
dc.subject filter-banks en_US
dc.subject instantaneous power spectrum en_US
dc.subject time-frequency energy density en_US
dc.subject Wigner-Ville distribution en_US
dc.subject linear FM asymptotic signal en_US
dc.subject BT product en_US
dc.subject TFDs en_US
dc.subject IF law en_US
dc.subject TD law en_US
dc.subject signal kernel en_US
dc.subject Central finite difference en_US
dc.subject CFD en_US
dc.subject Wigner-Distribution en_US
dc.subject marginal conditions en_US
dc.subject instantaneous autocorrelation function en_US
dc.subject analytic associate en_US
dc.subject linear FM WVD en_US
dc.subject dechirping en_US
dc.subject Doppler en_US
dc.subject time-frequency limiting en_US
dc.subject windowed WVD en_US
dc.subject filtered WVD en_US
dc.subject time-varying power spectral density en_US
dc.subject non-stationary random processes en_US
dc.subject wiener-khintchine theorem en_US
dc.subject evolutive spectrum en_US
dc.subject STFT en_US
dc.subject spectrogram en_US
dc.subject cross-terms en_US
dc.subject artifacts en_US
dc.subject artefacts en_US
dc.subject time-frequency smearing en_US
dc.subject time-frequency ridge en_US
dc.subject logon en_US
dc.subject Gabor transform en_US
dc.subject filter-bank en_US
dc.subject sonograph en_US
dc.subject sonogram en_US
dc.subject running transform en_US
dc.subject running energy spectrum en_US
dc.subject Page distribution en_US
dc.subject time-frequency gradient en_US
dc.subject Kirkwood-Rihaczek Distribution en_US
dc.subject Complex time-frequency energy density en_US
dc.subject marginal conditions en_US
dc.subject time-frequency support en_US
dc.subject Levin Distribution en_US
dc.subject Real time-frequency energy density en_US
dc.subject Margenau-Hill distribution en_US
dc.subject windowed Rihaczek distribution en_US
dc.subject windowed Levin distribution en_US
dc.subject IAF en_US
dc.subject time-lag kernel en_US
dc.subject MBD en_US
dc.subject Modified B distribution en_US
dc.subject quadratic TFDs en_US
dc.title Heuristic Formulation of Time-Frequency Distributions en_US
dc.type Book chapter en_US

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