Generalized lapped orthogonal transform with unequal-length basis functions

In this paper, the theory, design, and implementation of the Generalized Lapped Orthogonal Transform (GenLOT) with unequal-length basis functions are investigated. Necessary constraints on the building blocks which lead to the reduction of the degrees of design freedom is explained along with other trade-offs. Our main motivation of the new transform is its application in block-based image coding. Besides having all of the attractive properties of other lapped orthogonal transforms, this new class of GenLOT takes advantage of its long basis functions to reconstruct smooth signal and to reduce blocking artifacts, while its short basis functions are used to represent edges and reduce ringing. Design and image coding examples are presented to confirm the validity of the theory.