Time-frequency signal analysis and synthesis algorithms.

Abstract

This thesis addresses the issue of high resolution time-frequency representations of signals. Particular attention is paid to the issue of interference reduction while maintaining high resolution. Some new or extended time-frequency representations (TFR) are presented, including the Reduced Interference Distribution (RID), the variable-windowed Short Time Fourier Transform (VWSTFT), and the variable-windowed spectrogram (VWS). The RID and the VWS are members of Cohen's class of generalized time-frequency distributions. A systematic procedure to generate the RID kernel (or equivalently, to compute the RID) is proposed. Using the VWSTFT and VWS, the link between the short-time Fourier transform, Cohen's class, and the wavelet transform is investigated. An extended definition of the generalized discrete-time time-frequency distribution is proposed. This definition uses the full information in the discrete-time signal. Furthermore, a novel discrete-time kernel, called the "Binomial Kernel", and an associated VLSI architecture are proposed for fast implementation of a RID. Time-varying filtering and signal synthesis based on various TFR's is discussed. In particular, we suggest the use of the full outer product table in order to improve the performance of the WD-based methods. The extended discrete-time Wigner distribution is adopted as the model TFR for this purpose.