Practical considerations on optimising multistage decimation and interpolation processes

Multistage filter design is a complex multidimensional optimisation problem. The formulae for optimal design generally yield non-integer real numbers for the sample-rate-changing factors of multiple stages. Approaches yielding useful integer results have high computational cost and do not consider important multistage filter design properties. We have developed a simplified algorithm for directly searching the optimal integer results. Considering the most useful practical design parameters, optimal results can be approximated with a limited number of sets for any designs satisfying certain constraints, with negligible costs. This vastly simplifies the complexity of the problem.