Canonical signed digit representation for FIR digital filters

It is shown that the use of a canonical signed digit (CSD) representation of the filter coefficients can significantly reduce the complexity of the hardware implementation of digital FIR filters. This paper presents an example filter design that shows the error involved in limiting the number of allowable non-zero CSD coefficients for a real FIR bandpass filter. If not done carefully, brute force limiting can lead to large errors in the frequency response. The error is evaluated for varying numbers of non-zero CSD coefficients. Lastly, a system level architecture with a multiplier utilizing the properties of the CSD number representation system is proposed.