Design of 2-D $M$th Band Lowpass FIR Eigenfilters With Symmetries

In this letter, we extend the eigenfllter filter design method for the design of two-dimensional Mth band lowpass filters, with the filter impulse response having quadrantal or diagonal symmetry. We show that imposing the Mth band and symmetry constraints puts restrictions on the possible choices of the matrix M. We identify sufficient conditions on M, and show a class of matrices satisfying those conditions, so that Mth band lowpass filters with quadrantal or diagonal symmetry can be designed.