Time-frequency analysis of time localizable linear transform based on DFT

A class of new orthogonal transforms, time localizable linear transform (TLLT), which is constructed from a traditional linear transform and gives the nonuniform time-frequency tiling was introduced by authors. Time localizable DFT (TLDFT) is a subclass of TLLT constructed from DFT. In this paper, we are concerned with time-frequency characteristics of TLDFT bases to analyze qualitatively the performance of TLDFT in the time-frequency decomposition. Specially we investigate their phase characteristic since TLDFT bases concentrate their energies into the associated time locations and are inherently non-symmetric over the entire transform length