High-resolution signal synthesis for time-frequency distributions

Bilinear time-frequency distributions (TFDs) offer improved resolution over linear time-frequency representations (TFRs), but many TFDs are costly to evaluate and are not associated with signal synthesis algorithms. The spectrogram (SP) decomposition and weighted reversal correlator decomposition have been used to define low-cost, high-resolution TFDs. The authors show that the vector-valued square-root of a TFD (VVTFR) provides a representational underpinning for the TFD. By synthesizing signals from modified VVTFRs, they define high-resolution signal synthesis algorithms associated with TFDs. The signal analysis and synthesis packages can be implemented as weighted sums of SP/short-time Fourier transform (STFT) signal analysis and synthesis packages. The algorithms exhibit desirable properties, and yield results superior to STFT signal synthesis for a simple example.<>