On "slant-like" fast orthogonal transforms of arbitrary order

A concept for the construction of fast orthogonal transforms with matrices containing one or more predefined rows is proposed. In particular, two new families of "slant-like" transforms with matrices of arbitrary orders, including a constant row and a slant row of arbitrary slanting angle, are introduced. Transforms from these families may be computed with fast regular algorithms suitable for parallel implementation with a unified VLSI architecture that may be tuned to every representative of the family. An example of a new slant-like transform of order seven is also presented.