Design of programmable FIR filters using Canonical Double Based Number Representation

Scalability of current programmable FIR filter design methods are severely limited by the huge search space for common subexpressions and the density of unique subexpressions over the complete range of integers of desirable precision. This paper presents the first attempt to solve this problem by means of Canonical Double-Based Number Representation (CDBNR). We address the representation sparsity of generic filter coefficients by developing a simplified CDBNR search algorithm. The statistics generated for all double base products of a given coefficient word length are used to maximize the sharing of arithmetic operators and reduce the multiplexing cost. The effectiveness and scalability of the proposed design algorithm are demonstrated using two design examples. For the 8-bit programmable filter example implementable by two latest design methods, our proposed solution saves about 24% of arithmetic operator and multiplexer costs for large filter.