Fourth-order structures for multiplierless realizations of bandpass and bandstop digital filters transformed from all-pole lowpass filters

In our earlier investigations on developing multiplierless structures for recursive digital filters, we have demonstrated that utilizing low-sensitivity structures and appropriate transformations enable us to develop multiplierless implementations for bandpass and bandstop filters. In this paper, we present results for the structure that employs the low-sensitivity characteristics of the structures of the all-pole type for developing multiplierless implementations of bandpass and bandstop digital recursive filters transformed from all-pole lowpass filters. The schemes are quite attractive when we allow marginal deviations in the specifications compared to initial specifications or we start with a design having marginally stricter specifications than the desired specifications without any increase in the filter order. This leads to a quite low number of nonzero bits, as is shown by means of illustrative examples.