On discrete cosine transform

TL;DR

This paper introduces a generalized discrete cosine transform with three parameters, proves its orthogonality in new cases, and also proposes a generalized discrete W transform, expanding the theoretical framework of signal processing transforms.

Contribution

It presents a novel generalized DCT and W transform with parameterization, along with proofs of their orthogonality in new cases, enhancing transform design options.

Findings

Proposed a generalized DCT with three parameters.

Proved orthogonality of the new DCT in specific cases.

Introduced a generalized discrete W transform with orthogonality proofs.

Abstract

The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In simulating the discrete cosine transform, we propose a generalized discrete cosine transform with three parameters, and prove its orthogonality for some new cases. A new type of discrete cosine transform is proposed and its orthogonality is proved. Finally, we propose a generalized discrete W transform with three parameters, and prove its orthogonality for some new cases.