Optimal Filter Designs for Separating and Enhancing Periodic Signals

In this paper, we consider the problem of separating and enhancing periodic signals from single-channel noisy mixtures. More specifically, the problem of designing filters for such tasks is treated. We propose a number of novel filter designs that 1) are specifically aimed at periodic signals, 2) are optimal given the observed signal and thus signal adaptive, 3) offer full parametrizations of periodic signals, and 4) reduce to well-known designs in special cases. The found filters can be used for a multitude of applications including processing of speech and audio signals. Some illustrative signal examples demonstrating its superior properties as compared to other related filters are given and the properties of the various designs are analyzed using synthetic signals in Monte Carlo simulations.