Phasor-Banks: Customizable filter banks for robust dynamic time-frequency analysis

The paper extends the concept of dynamic phasors to allow customizations that could benefit a number of diverse applications. Connections between dynamic phasors and non-decimated filter banks are established in discrete time, and links with the Gabor transform are presented. The fundamental filter bank structure that includes an analysis and a synthesis family of filters is described next. In the presented context this structure naturally leads to introduce the concept of Phasor-Banks, a family of non-decimated perfect reconstruction filter banks for dynamic (online, one sample at a time) time-frequency analysis and modeling. We analyze in detail properties of windowed finite impulse response (FIR) phasor banks, introduce the concept of robustness with respect to perturbations of dynamic phasors, and derive conditions for optimally robust phasor banks. This allows us to further extend the concept of phasor banks to allow for infinite impulse response (IIR) analysis and synthesis filters.