Reassignment and synchrosqueezing for general time-frequency filter banks, subsampling and processing

In this contribution, we extend the reassignment method (RM) and synchrosqueezing transform (SST) to arbitrary time-frequency localized filters and, in the first case, arbitrary decimation factors. A sufficient condition for the invertibility of the SST is provided. RM and SST are techniques for deconvolution of short-time Fourier and wavelet representations. In both methods, the partial phase derivatives of a complex-valued time-frequency representation are used to determine the instantaneous frequency and group delay associated to the individual representation coefficients. Subsequently, the coefficient energy is reassigned to the determined position. Combining RM and frame theory, we propose a processing scheme that benefits both from the improved localization of the reassigned representation and the frame properties of the underlying complex-valued representation. This scheme is particularly interesting for applications that require low redundancy not achievable by an invertible SST.