A novel modified branch-and-bound technique for discrete optimization over canonical signed-digit number space

Abstract

A novel algorithm is presented for the design of DSP systems by optimization using the branch-and-bound technique over the canonical signed-digit (CSD) multiplier coefficient space. The proposed algorithm has two main salient features: (1) For a given infinite-precision decimal floating radix-point multiplier coefficient x, it can directly provide the corresponding decimal floating radix-point values for the smallest representable CSD coefficient greater than x and the largest representable CSD coefficient less than x, where these CSD coefficients have pre-specified wordlength and number of nonzero digits. (2) It does not make any recourse to conversion from CSD to decimal, and vice versa, from decimal to CSD conversion. The proposed algorithm finds applications in the optimization of multi-rate IIR or FIR digital filters over the CSD coefficient space.