Fast linearly independent arithmetic expansions

The concept of Linearly Independent arithmetic (LIA) transforms and expansions is introduced in this paper. The recursive ways of generating forward and inverse fast transforms for LIA are presented. The paper describes basic properties and lists those LIA transforms which have convenient fast forward algorithms and easily defined inverse transforms. In addition, those transforms which require horizontal or vertical permutations to have fast transform are also discussed. The computational advantages and usefulness of new expansions based on LIA logic in comparison to known arithmetic expansions are discussed.