Design of signal word decomposed filters with canonical-signed digit coefficients

To reduce the computational complexity of FIR digital filters while keeping their performance, two techniques are combined; signal word decomposed filter (SWDF) concept and canonical-signed digit (CSD) representation for their coefficients. The binary expressed input signal word is divided into more significant and less significant parts, and they are processed by different subfilters; longer subfilter for the more significant part and shorter subfilter for the less significant part. Each filter has its coefficient represented by CSD numbers so that multiplications are performed by wired shifts and addition/subtraction. The design of such filters is highly complicated and the genetic algorithm (GA) is used. A special coding method is proposed to reduce the designing time. It is confirmed that the proposed method has the synergistic effect of the two techniques