On multistage finite impulse response (FIR)filters with decimation

Nonrecursive, finite impulse response (FIR) digital filters are known to require a reduced rate of arithmetic operations relative to recursive infinite impulse response filters (IIR) in many applications where the sample rate is to be diminished. FIR symmetry and the absence of state variables contribute to the efficiency. A significant further economy in both arithmetic and memory space can be achieved by realizing the desired filter as a cascade of FIR stages, with interstage decimation of sample rate. In this paper, an approach to optimally allocate (i.e., factor) the composite decimation among filter stages (and hence determine the filter state characteristics) is described.