2-D Hartley transforms

Abstract

Two different versions of kernels associated with the 2-D Hartley transforms are investigated in relation to their Fourier counterparts. This newly emerging tool for digital signal processing is an alternate means of analyzing a given function in terms of sinusoids and is an offshoot of Fourier transform. Being a real‐valued function and fully equivalent to the Fourier transform, the Hartley transform is more efficient and economical than its progenitor. Hartley and Fourier pairs of complete orthogonal transforms comprise mathematical twins having definite physical significance. The direct and inverse Hartley transforms possess the same kernel, unlike the Fourier transform, and hence have the dual distinction of being both self reciprocal and having the convenient property of occupying the real domain. Some of the properties of the Hartley transform differ marginally from those of the Fourier transform.