Design of Linear-Phase FIR Multiple-Notch Filters via an Iterative Reweighted OMP Scheme

This brief considers the design of sparse linear-phase finite-impulse-response multiple-notch filters whose notch frequencies are arbitrarily spaced across the spectrum [0, π]. The proposed scheme, i.e., iteratively reweighted orthogonal matching pursuit (IROMP), is based on the orthogonal matching pursuit performed under the weighted l₂-norm whose weights are iteratively computed through the hybrid l₁/l₂-norm minimization. At each iteration, the IROMP is employed to yield the filter whose response best approximates the desired filter. The computed filter is then modified through solving a linear programming problem. The iteration stops when the modified filter meets the design specifications. The simulation demonstrates the potentials of the IROMP scheme.