Efficient multistage implementation of rational sampling rate converter

In Digital audio processing, there are multiple standard sampling rates, for example, 48kHz for studio work, 44.1kHz for compact disk(CD) mastering. Therefore, sampling rate conversion is needed to interchange signals from one field to another. A rational sampling rate conversion by L/M can be done cascading an L-fold up-sampler and an M-fold down-sampler with a linear phase FIR lowpass filter in the middle. When both L and M have large values, the lowpass filters are required to have an extremely narrow normalized bandwidth and a sharp transition characteristic, causing difficulty in design and implementation. This paper describes a technique to overcome this difficulty for the case both L and M are composite numbers, giving an multistage converter structure where each stage is consisting of an up-sampler and a down-sampler, both of a small conversion ratios, with a filter having not so sharp normalized transition characteristic in the middle, remarkably reduced total computation complexity.