Fastest linearly independent arithmetic transforms and their calculation on systolic array processors

Fastest linearly independent arithmetic (LIA) transforms have computational costs that are lower than that of the standard arithmetic transform. They also possess fast direct and inverse transforms that enable their efficient calculation using fast transform and make them suitable for systolic array implementation. Calculation of fastest LIA transform spectral coefficients by systolic array processor is described here. New fastest LIA transforms are introduced and various properties that are relevant to the fastest LIA transform spectra calculation are presented. General steps for deriving the linear systolic array structures are listed and examples are given for several previous and new fastest LIA transforms. It is shown that the number of linear systolic array structures required for obtaining the best fastest LIA transform is smaller than the number of all possible fastest LIA transforms. Experimental results for the fastest LIA transforms are also shown and compared with the standard arithmetic transform. The comparison shows that the fastest LIA transforms have smaller numbers of non-zero spectral coefficients for many binary functions