The use of finite group presentations in signal processing has not been exploit in the current literature. Based on the existing signal processing algorithms (not necessarily group theoretic approach), various signal processing transforms have unique decomposition capabilities, that is, different types of signal has different transformation combination. This paper aimed at studying representation of finite groups via their actions on Signal space and to use more than one transformation to process a signal within the context of group theory. The objective is achieved by using group generators as actions on Signal space which produced output signal for every corresponding input signal. It is proved that the subgroup presentations act on signal space by conjugation. Hence, a different approach to signal processing using group of transformations and presentations is established.

A long-standing problem is how to create a short-length presentation for finite groups of degree n. This paper aimed at presenting a concrete method for generating presentations for the groups Sm+n, S2m and Smn for all m,nÎZ+ with fewer relations than the existing literature from the presentations of Sm and Sn. The aim is achieved by considering finite groups acting on sets and Cartesian product of groups which lead to the construction of multiple transformations as representatives of some finite groups.

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