Design of 2-D PCAS digital filters based around restrictive and highly restrictive coefficient sets

This paper addresses the problem of designing 2-D filters composed of a Parallel Connection of All-pass Subfilters (PCAS). The PCAS filters have finite wordlength coefficients which are based on subsets of straight coefficient ranges. Restrictive coefficient sets, typically 6 bits or less, based on a signed digit number system are compared to full range coefficients. Examples are given, based on the use of a simulated annealing algorithm and a modified Hooke and Jeeves algorithm. Designs based around powers-of-two coefficients and sum of powers-of-two coefficients are examined. Furthermore, an algorithm is developed to minimise the number of non-zero bits in each coefficient whilst optimising for minimum error. The implications of these results for hardware implementation are discussed.<>