Multidimensional Fourier and Hartley Transforms—Are They Same?

Abstract

Multidimensional Hartley transforms with two different kernels namely the multi kernel and single kernel versions and their relation with the multidimensional Fourier transform are investigated. The multi kernel multidimensional Hartley transform is mathematically correct and it is equally applicable to all fields. On the other hand the single kernel representation of the multidimensional Hartley transform is mathematically incorrect despite the fact that it is fully equivalent to the multidimensional Fourier transform. Therefore, mathematically incorrect version of the multidimensional Hartley transform with a single kernel representation and the corresponding Fourier transform are not the same.

Indexing terms:

• Fourier transforms
• Hartley transforms
• Discrete transform
• Complex
• Real
• Kernel

Additional information

Notes on contributors

N Sundararajan

Narasimman Sundararajan, had graduated in Mathematics from the University of Madras and subsequently obtained his Master's degree in Geophysics and PhD from Osmania University in 1978 and 1982 respectively. Currently he is an Associate Professor at Centre of Exploration Geophysics, Osmania University.

His PhD thesis covers an extensive application of the Hilbert transform to processing and interpretation of geophysical data. He has published over 40 research papers in the leading International Journals besides being a reviewer for many International Journals. He has guided several students for their PhD. Dr Sundararajan had associated with the Theoretical Geophysics Group of National Geophysical Research Institute (CSIR Lab) as a Scientist for a short while during 1983–1984.

His current research interests are signal processing, image processing, development of tools and techniques for processing and interpretation of geophysical data, software, prediction seismology and has a specific interest in speech signal processing.

S Vijayachitra

S Vijayachitra, had graduated in Physics from the University of Madras in 1989 and obtained her Master's degree in 1991. She did her graduation as well as Master's from Meenakshi College, Chennai. She is a recipient of Gold Medal from the University of Madras.

Later she did her Honors in System Management in NIIT from Madras and employed as Software Engineer for quite some time before switching over as a Faculty in Pentagon Computer Academy.

Her current interest is mainly in development of software for commercial as well as scientific applications. She has a specific interest in Applied Mathematics and French.