Arbitrary factorisation of decimation ratio for efficient multistage realisation

Multistage implementation of decimators is in many cases more efficient than single-stage one. However, if the decimation ratio is prime, it cannot be factorised into a product of smaller integer factors. Previously it has been proposed that a rational decimation stage can be used to enable arbitrary selection of the decimation ratios. This way the advantages of multistage decimation and special filter structures such as halfband filters become available regardless of the overall decimation ratio. In this paper, we propose a method for optimising the overall response of such multistage decimators. Imaging and aliasing phenomena in such decimators are analysed, an iterative design method is introduced, and design examples are given. The proposed method can also be used for non-prime decimation ratios when their prime factors are not favourable for multistage implementation.