Optimum FIR Digital Filter Implementations for Decimation, Interpolation, and Narrow-Band Filtering

Abstract-In this paper a general theory of multistage decimators and interpolators for sampling rate reduction and sampling rate increase is presented. A set of curves and the necessary relations for optimally de-signing multistage decimators is also given. It is shown that the pro-cesses of decimation and interpolation are duals and therefore the same set of design curves applies to both problems. Further, it is shown that highly efficient implementations of narrow-band finite impulse response (FIR) fiiters can be obtained by cascading the processes of decimation and interpolation. Examples show that the efficiencies obtained are comparable to those of recursive elliptic filter designs. W I