When large reductions in sampling rates are required, the design of adequate decimation filters becomes more difficult, usually resulting in filters with a prohibitively large number of taps. This note introduces multistage decimators that accomplish large reductions in sampling rate as a sequence of several smaller reductions. In a properly designed multistage approach, the filters for all the stages have a total tap count that is significantly lower than the filter tap count needed to obtain similar performance from a single-stage implementation.
When the desired decimation factor, M, can be expressed as a product of I positive integer factors
M = M1 M2 ... MI
the desired decimation can be realized as a cascade ...