Optimal FIR filters with almost linear phase

Abstract

FIR filters are known to be stable and have a linear phase when symmetry properties, e.g., h[n]=h[M-n], are kept. A common FIR filter design method is the Parks-McClellan algorithm. In this algorithm, linear phase FIR filters, which are optimal in the minimax sense, are designed. These filters have the form of H(/spl omega/)=A(/spl omega/)e/sup j(/spl beta/-/spl omega//spl alpha/)/, where A(/spl omega/) is real, /spl alpha/ is an integer or an integer plus 1/2 and /spl beta/ is 0 or /spl pi//2. These FIR filters are always symmetric or antisymmetric. We introduce a simple procedure for designing almost linear phase FIR filters, having a similar form to H(/spl omega/), but an arbitrary /spl alpha/, that are optimal in a similar sense.