Generalized fastest linearly independent arithmetic transforms

A pair of fastest linearly independent arithmetic (LIA) transforms and their properties have been discussed in recent papers. The transforms have the smallest computational complexities among all LIA transforms that have been introduced and their spectra can be calculated efficiently using fast transforms. An extension of the fastest LIA transforms, to produce new LIA transforms, is proposed. The new transforms have the same computational complexity as the existing fastest LIA transforms and their fast forward and inverse transforms can be easily calculated. Some properties for the new fastest LIA transforms are also presented here.