Integrated representation for discrete Fourier and wavelet transforms using vector notation

  • Tariq Javid Department of Biomedical Engineering, Faculty of Engineering Sciences and Technology, Hamdard University, Karachi Pakistan
  • Muhammad Faris Department of Biomedical Engineering, Faculty of Engineering Sciences and Technology, Hamdard University, Karachi Pakistan
  • Arshad Aziz Department of Electronic and Power Engineering, National University of Sciences and Technology, Karachi Campus, Pakistan
  • Pervez Akhtar Department of Electrical Engineering, Sir Syed University of Engineering and Technology, Karachi Pakistan

Abstract

Many mathematical operations are implemented easily through transform domain operations. Multiple transform domain operations are used independently in large and complex applications. There is a need to develop integrated representations for multiple transform domain operations. This paper presents an integrated mathematical representation for the discrete Fourier transformation and the discrete wavelet transformation. The proposed combined representation utilizes the powerful vector notation. A mathematical operator, called the star operator, is formulated that merges coefficients from different transform domains. The star operator implements both convolution and correlation processes in a weighted fashion to compute the aggregated representation. The application of the proposed mathematical formulation is demonstrated successfully through merging transform domain representations of time-domain and image-domain representations. Heart sound signals and magnetic resonance images are used to describe transform-domain data merging applications. The significance of the proposed technique is demonstrated through merging time-domain and image-domain representations in a single- stage that may be implemented as the primary processing engine inside a typical digital image processing and analysis system.

Published
Jul 1, 2022
How to Cite
JAVID, Tariq et al. Integrated representation for discrete Fourier and wavelet transforms using vector notation. Mehran University Research Journal of Engineering and Technology, [S.l.], v. 41, n. 3, p. 175-184, july 2022. ISSN 2413-7219. Available at: <https://publications.muet.edu.pk/index.php/muetrj/article/view/2533>. Date accessed: 15 apr. 2024. doi: http://dx.doi.org/10.22581/muet1982.2203.18.
Section
Articles
This is an open Access Article published by Mehran University of Engineering and Technolgy, Jamshoro under CCBY 4.0 International License