Multiplierless implementation of bandpass and bandstop recursive digital filters using allpass structures

Under certain conditions an odd-order lowpass or highpass recursive digital filter can be decomposed into a sum of two allpass filters with real coefficients. This decomposition has the attractive property that there exist for its implementation structures where both the number of delays and the number of multipliers are equal to the filter order, thereby making the overall implementation very efficient. This paper develops some second- and fourth-order allpass structures that combine this property for generating multiplierless implementations for an odd-order recursive digital filter along with transformations from a prototype lowpass filter to a bandpass or bandstop filter. Utilizing these structures along with allowing some marginally insignificant deviations in the specifications such as in the passband and stopband tolerances, the total number of nonzero bits for multiplier coefficients, i.e., those of shifts and adds and/or subtracts, becomes quite small. This makes the proposed approach very attractive. Alternatively, the prototype lowpass filter can be designed with marginally stricter tolerances than the desired specifications such that it meets the given criteria after quantizing the filter coefficients.