The notions of time, frequency, and scale are generalized using concepts from unitary operator theory and applied to time-frequency analysis, in particular the wavelet and short-time Fourier transform orthonormal bases and Cohen's class of bilinear time-frequency distributions. The result is an infinite number of new signal analysis and processing ...

Unitary similarity transformations furnish a simple yet powerful vehicle for generating new classes of joint distributions based on concepts different from time, frequency, and scale. These new signal representations focus on the critical characteristics of large classes of signals and, hence, prove useful for representing and processing signals ...

The proportional-bandwidth and constant-bandwidth time-frequency signal decompositions of the wavelet, Gabor, and Wilson orthonormal bases have attracted substantial interest for representing nonstationary signals. However, these representations are limited in that they are based on rectangular tessellations of the time-frequency plane. While much ...

We consider the design of kernels for time-frequency distributions through the phase, rather than amplitude, response. While phase kernels do not attenuate troublesome cross-components, they can translate them in the time-frequency plane. In contrast to previous work on phase kernels that concentrated on placing the cross- components on top of the ...

Time-frequency representations with fixed windows or kernels figure prominently in many applications, but perform well only for limited classes of signals. Representations with signal- dependent kernels can overcome this limitation. However, while they often perform well, most existing schemes are block-oriented techniques unsuitable for on-line ...

The generalized entropies of Renyi inspire new measures for estimating signal information and complexity in the time-frequency plane. When applied to a time-frequency representation (TFR) from Cohen's class or the affine class, the Renyi entropies conform closely to the notion of complexity that we use when visually inspecting time-frequency images. ...

In this paper, we introduce a new set of tools for time-varying spectral analysis: the pseudo affine Wigner distributions. Based on the affine Wigner distributions of J. and P. Bertrand, these new time-scale distributions support efficient online operation at the same computational cost as the continuous wavelet transform. Moreover, they take advantage ...

We propose a straightforward characterization of all quadratic time-frequency representations covariant to an important class of unitary signal transforms (namely, those having two continuous-valued parameters and an underlying group structure). Thanks to a fundamental theorem from the theory of Lie groups, we can describe these representations ...

Time-frequency distributions (TFDs), which indicate the energy content of a signal as a function of both time and frequency, are powerful tools for time-varying signal analysis. The lack of a single distribution that is "best" for all applications has resulted in a proliferation of TFDs, each corresponding to a different, fixed mapping from signals ...

Using the Wigner distribution, we derive and analyze a matrix formulation for the chirplet transform, a signal analysis tool that generalizes the wavelet and short-time Fourier transforms. The formulation expresses the translations, scalings, and shears of the chirplet transform in terms of affine matrix transformations on the time-frequency plane. ...