Publication

Bilinear time-frequency representation of signals: The shift-scale invariant class

Rüdiger Urbanke
1994
Journal Articles

Abstract

The class of bilinear time-frequency representations (BTFR's) that are invariant (or covariant) to time shifts, frequency shifts, and time-frequency scalings. This shift-scale invariant class is the intersection of the classical shift-invariant (Cohen) class and the recently defined affine class. The mathematical description of shift-scale invariant BTFR's is in terms of a 1-D kernel and is thus particularly simple. The paper concentrates on the time-frequency localization properties of shift-scale invariant BTFR's. Since any shift-scale invariant BTFR is a superposition of generalized Wigner distributions, the time-frequency localization of the family of generalized Wigner distributions is studied first. For those shift-scale invariant BTFR's that may be interpreted as smoothed versions of the Wigner distribution (e.g., the Choi-Williams distribution), an analysis in the Fourier transform domain shows interesting peculiarities regarding time-frequency concentration and interference geometry properties

Official source

https://infoscience.epfl.ch/entities/publication/9fa61be1-25fa-4711-b14f-c5efbd17ccfc

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Rüdiger Urbanke
1994
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/9fa61be1-25fa-4711-b14f-c5efbd17ccfc

About this result

Related concepts (32)

Bilinear time–frequency distribution

Bilinear time–frequency distributions, or quadratic time–frequency distributions, arise in a sub-field of signal analysis and signal processing called time–frequency signal processing, and, in the statistical analysis of time series data. Such methods are used where one needs to deal with a situation where the frequency composition of a signal may be changing over time; this sub-field used to be called time–frequency signal analysis, and is now more often called time–frequency signal processing due to the progress in using these methods to a wide range of signal-processing problems.

Time–frequency analysis

In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations. Rather than viewing a 1-dimensional signal (a function, real or complex-valued, whose domain is the real line) and some transform (another function whose domain is the real line, obtained from the original via some transform), time–frequency analysis studies a two-dimensional signal – a function whose domain is the two-dimensional real plane, obtained from the signal via a time–frequency transform.

Time–frequency representation

A time–frequency representation (TFR) is a view of a signal (taken to be a function of time) represented over both time and frequency. Time–frequency analysis means analysis into the time–frequency domain provided by a TFR. This is achieved by using a formulation often called "Time–Frequency Distribution", abbreviated as TFD. TFRs are often complex-valued fields over time and frequency, where the modulus of the field represents either amplitude or "energy density" (the concentration of the root mean square over time and frequency), and the argument of the field represents phase.

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Bilinear time-frequency representation of signals: The shift-scale invariant class

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