A simple commutativity condition for block decimators and expanders

Commutativity rules play an essential role when building multirate signal processing systems. In this letter, we focus on the interchangeability of block decimators and expanders. We, formally, prove that commutativity between these two operators is possible if and only if the data blocks are of an equal length corresponding to the greatest common divisor of the integer decimation and expansion factors. Index Terms Block sampling, Decimation, Commutativity, Expansion.