Optimized Multistage Decimation Based on Optimal Factorization of Decimation Ratio

In this paper, we analyze a method for designing an optimized multistage decimation filter chain focused on minimizing computational load. Decimation ratios for each of the K stages are determined to achieve the optimal number of filter multiplications per second. To enable the optimal factorization of non-integer or prime decimation ratios, the first stage of the decimation chain is designed to perform non-integer decimation using a transposed modified Farrow structure. We evaluate the performance of the optimized multistage filter chain with varying numbers of stages and compare it to an optimal FIR realization. The results demonstrate that the Farrow structure significantly reduces the computational load for prime and non-integer decimation cases and benefits non-prime cases.