Time-frequency analysis using warped-based high-order phase modeling
EURASIP Journal on Applied Signal Processing
Digital Signal Processing
Techniques to obtain good resolution and concentrated time-frequency distributions: a review
EURASIP Journal on Advances in Signal Processing
Fast computation of frequency warping transforms
IEEE Transactions on Signal Processing
Localization in underwater dispersive channels using the time-frequency-phase continuity of signals
IEEE Transactions on Signal Processing
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We consider scale-covariant quadratic time-frequency representations (QTFRs) specifically suited for the analysis of signals passing through dispersive systems. These QTFRs satisfy a scale covariance property that is equal to the scale covariance property satisfied by the continuous wavelet transform and a covariance property with respect to generalized time shifts. We derive an existence/representation theorem that shows the exceptional role of time shifts corresponding to group delay functions that are proportional to powers of frequency. This motivates the definition of the power classes (PCs) of QTFR's. The PCs contain the affine QTFR class as a special case, and thus, they extend the affine class. We show that the PCs can be defined axiomatically by the two covariance properties they satisfy, or they can be obtained from the affine class through a warping transformation. We discuss signal transformations related to the PCs, the description of the PCs by kernel functions, desirable properties and kernel constraints, and specific PC members. Furthermore, we consider three important PC subclasses, one of which contains the Bertrand (1992) Pk distributions. Finally, we comment on the discrete-time implementation of PC QTFRs, and we present simulation results that demonstrate the potential advantage of PC QTFRs