Towards new small-kernel-based discrete orthogonal transforms and their algorithmic implementation

This note presents a simple and practical idea for synthesizing new discrete orthogonal transform (DOT) algorithms based on the properties of the Kronecker product of a sequence of orthogonal matrices. Specifically, it exploits the fact that the Kronecker product of orthogonal matrices is itself orthogonal. The proposed approach utilizes small-sized DOT kernels to construct new algorithms. By skillfully choosing kernels, one can create new orthogonal bases and simultaneously construct fast algorithms for discrete transforms in these new bases.