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Signal-Dependent Time-Frequency Analysis using a Radially Gaussian Kernel
Time-frequency distributions are two-dimensional functions that indicate the time-varying frequency content of one-dimensional signals. Each bilinear time-frequency distribution corresponds to a kernel function that ...
Shear Madness: New Orthonormal Bases and Frames Using Chirp Functions
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, ...
Warped Wavelet Bases: Unitary Equivalence and Signal Processing
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 ...
A Signal Dependent Time Frequency Representation: Optimal Kernel Design
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 ...
Signal Transform Covariant to Scale Changes
A unitary signal transformation that is covariant by translation to scale changes (dilations and compressions) in the signal is formulated and justified. Unlike the Mellin transform, which is invariant to scale changes, ...