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Using variable length 13-ary, radix-4 CSD coefficients to achieve low-area implementations of FIR filters

Coefficient representations in the Canonical-Signed-Digit (CSD) number system are widely used, because they lead directly to efficient addition/subtraction networks for implementation of weighted sums of 2's-complement input signals in FIR filters. A recent radix-4 generalization of CSD can dramatically reduce network sizes. By combining radix-4 representations of coefficients with techniques for assigning different numbers of bits to different coefficients, we further reduce the area required for implementation. We draw the conclusion from our data that this process can reduce the space required for implementing these kinds of filters; however, a better approach might be to design filters with coefficients that are readily represented in the number representation scheme before implementation.