Computer Simulation Results and Analysis for a Root-Raised Cosine Filter Design using Canonical Signed Digits

Abstract

Filters implemented using Canonical Signed-Digit (CSD) number representation for the coefficients have been studied for many years as an efficient way to increase the speed and reduce the hardware complexity. A simple and very effective method for designing a CSD filter with a specific set of filter parameters has been investigated and its simulation results are presented here. In order to optimize filter coefficients into the corresponding CSD numbers, the Minimum Mean Square Error (MMSE) criterion is used. Furthermore, an attempt is made to improve frequency response of the CSD filter by allocating an extra non-zero digit for normalized coefficients exceeding one-half. Due to limited filter aperture width in examples presented here, the frequency response of CSD filter as the number of non-zero digits in a CSD code increases is not affected much. A root-raised cosine filter model is employed as a base line for this design approach. Finally, the CSD filter simulation results and a hardware complexity comparison with a conventional filter are also shown along with the eye diagrams an Bit-Error-Rate (BER) performance curves.