Multiplierless realization of recursive digital filters using allpass structures

Under certain conditions, an odd-order lowpass or highpass recursive digital filter can be decomposed into the sum of two allpass filters with real coefficients. This decomposition has the attractive property that, for its implementation, there exist 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. The paper develops some allpass filter structures that combine this advantage with those of some low-sensitivity substitution and transformation blocks for replacing unit delay elements. These combinations enable one to generate multiplierless implementations for odd-order recursive digital filters and even-order bandpass and bandstop filters. 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, making this approach very attractive. Alternatively, the overall filter can be designed with marginally stricter tolerances than the desired specifications in such a manner that it meets the criteria after quantizing the filter coefficients.