Higher order sigma-delta modulation encoding for the design of efficient multiplierless FIR filters with powers-of-two coefficients

We present a technique for the design of multiplierless FIR filters with canonic signed digit (CSD) coefficients based on higher order sigma-delta modulation with a CSD quantizer (ΣΔ-CSD). The CSD quantizer yields FIR filter coefficients quantized to sums of a few signed powers-of-two digits, eliminating the need for multiplication. The sigma-delta modulation moves the quantization error out of the band of interest into a frequency band where the increased error can be attenuated by a cascaded prefilter in a prefilter-equalizer structure, or be attenuated by a decimation filter in a multi-rate approach. The use of higher order sigma-delta modulation provides more flexibility in moving the quantization error than the previously proposed first-order modulation. We give lowpass and bandpass examples where the filters designed by the higher order modulation demonstrate substantial frequency characteristic improvement. An empirical design guideline to ensure the stability for the higher order ΣΔ-CSD modulation is also given in the paper