Filtering in the joint time/chirp-rate domain for separation of quadratic and cubic phase chirp signals

This article investigates the possibility and convenience of a filtering operation in the joint time/chirp-rate (TCR) domain, and proposes a novel linear TCR filter for decomposing multicomponent signals into their quadratic and/or cubic phase chirp components with monotonic instantaneous chirp-rate (ICR) laws only. The TCR domain mask of the filter is selected on a display of a TCR representation of an input signal to isolate the desired chirp component. Projecting the input signal onto the phase signal associated with the TCR mask and approximating the phase difference in this projection operation in terms of ICR values result in the proposed TCR filter that recovers the selected component. Simulations illustrate the proposed filtering in recovery of undersampled cubic phase signals and in resolving back-to-back objects from in-line holograms for which cases it is easier to design filter masks in the TCR domain than in the time-frequency domain.