V/HS structure for transforms and their fast algorithms

Abstract

A general parameterized recursive matrix representation for a wide class of transforms with fast algorithm is suggested that allows to automatically generate an arbitrary transform from the family by selecting a specific set of parameters and to evaluate their computational complexity in a very straightforward way. A regular derivation of pruned transforms is also developed to generating arbitrarily pruned transforms for both, input and output arbitrary pruning. A Matlab code has been developed to test the correctness of algorithms, to evaluate their complexity, to generate their visual representation by flow charts and to automatically generate Matlab executable transform codes. It is demonstrated that these techniques allow also to easily derived fast algorithms for shifted transforms, DCT and transforms of real valued data.