Realization of Finite Impulse Response Filters Using Coefficients +1, 0, and -1

Abstract

New classes of nonrecursive linear digital filters are proposed as alternatives to conventional methods for digital signal processing devices. In fact, the traditional approach, where signal samples are represented by 8-15 bit words, can be very expensive to implement due to the complexity of multibit multipliers and adders. Filter structures consisting of a transversal filter with tap coefficients restricted to - 1, 0, or + 1 and cascaded with simple recursive sections are proposed. Using a mean square error criterion, dynamic programming methods to select optimum sets of coefficient values for the taps are presented and evaluated. It is shown that these structures lend themselves to very simple hardware implementations and offer a valid alternative to the conventional filtering approach. Designs for several example filters are presented, and their implementation complexity is examined.