MULTIPLICATIVE REALIZATION OF FIR SYSTEMS THAT IS LOGARITHMICALLY EFFICIENT.

A simple mathematical identity that expresses a power series as a product is used to obtain an efficient realization of a class of FIR filters. This class arises naturally when an approximation of an IIR filter is desired. The basic achievement is shown to be a logarithmic saving in the number of multipliers and in the round-off noise. This new synthesis of FIR filters is expected to be most valuable where the length of the FIR is large, as when the poles of the original IIR filter are close to the unit circle and in realizing nonminimal filters that are free of limit cycles efficiently. Also, linear phase FIR filters are expected to be efficiently implemented using this technique.