An Integer Approximation Method for Discrete Sinusoidal Transforms

TL;DR

This paper introduces a versatile integer approximation method for discrete sinusoidal transforms like DFT, DHT, and DCT, emphasizing low complexity and orthogonality, with new 8-point square wave transforms demonstrated.

Contribution

It presents a general dyadic rational approximation approach for discrete transforms, applicable to various sizes, improving flexibility over existing methods.

Findings

Transforms are computationally efficient with low multiplicative complexity.

Orthogonality can be achieved through matrix polar decomposition.

New 8-point square wave transforms are introduced as special cases.

Abstract

Approximate methods have been considered as a means to the evaluation of discrete transforms. In this work, we propose and analyze a class of integer transforms for the discrete Fourier, Hartley, and cosine transforms (DFT, DHT, and DCT), based on simple dyadic rational approximation methods. The introduced method is general, applicable to several block-lengths, whereas existing approaches are usually dedicated to specific transform sizes. The suggested approximate transforms enjoy low multiplicative complexity and the orthogonality property is achievable via matrix polar decomposition. We show that the obtained transforms are competitive with archived methods in literature. New 8-point square wave approximate transforms for the DFT, DHT, and DCT are also introduced as particular cases of the introduced methodology.