Quadratic FIR-filter design as a generalized eigenproblem

This work suggests optimizing quadratic performance measures on (possibly multi-rate) DSP systems in order to design one or more embedded FIR filters, which might be real or complex and with or without linear-phase, N-th band, or other structure. The outlined approach replaces the eigenproblem of the eigenfilter design method with a generalized eigenproblem. A general capability results for minimizing an arbitrary nonnegative-definite (purely) quadratic system-performance measure subject to a single arbitrary equality constraint on a second such quadratic. Using this one constraint to fix the impulse-response energy in nonembedded single-filter design results in the ordinary eigenfilter method. A simple example and a geometric interpretation show that alternate equality constraints can profoundly affect the solution. Finally a multirate matched-filtering-system example design impossible with the ordinary eigenfilter method hints at the flexibility of the approach.