Skip to Main Content
Low-complexity and high-speed design of infinite impulse response (IIR) filters focuses on minimizing the number of logic operators and the logic depth in the implementation of the coefficient multipliers. Although the Bull-Horrocks modified (BHM) and the n-dimensional reduced adder graph (RAGn) algorithms result in considerable reduction of logic operators (LO), it uses the highest logic depth (LD) and hence the resulting IIR filters are not optimized in view of filtering speed. The Hartley algorithm proposed for finite impulse response (FIR) filters offers a reduction in LD, but it requires additional LO respect to BHM technique. A method to minimize the number of LO and the LD in the multipliers of pulse-shaping IIR filters by efficiently combining Hartley's horizontal common subexpressions and vertical common subexpressions that occur across the filter coefficients is proposed here. Design examples of pulse-shaping filters employed in a dual-mode GSM/W-CDMA receiver show that our method offers reduction of complexity as well as delay when compared with earlier methods.