Development of Quantum Hartley Transform for Signal Processing Applications

Abstract

The present paper deals with the q-analogue of Hartley transform which is the q-extension of Hartley transform. It is an orthogonal transform which is defined in the domain -∞ to ∞ whose kernel is (cosinusidal) function ‘cas’ which is a combination of trigonometrical functions ‘sin’ and ‘cos’. The q-analogue of Hartley transform is defined in the domain -∞ to ∞ whose kernel is ‘cas_q’ function which is a q-extension of ‘cas’ function. In the similar manner ‘cas_q’ is a q-extension of combination of q-extension of trigonometrical functions ‘sin_q’ and ‘cos_q’ defined in Kack and Chengue book [18]. In this paper we will establish some basic properties of q-Hartley transform, for instance linear property, change of scale property.