A Comprehensive Toolset for Signal Processing using a Family of Hadamard Transforms

Dure Jabeen; Tahimna Khan; S. M. Ghazanfar Monir; Dilbar Hussain; Rumaisa Iftikhar

Authors

Dure Jabeen Department of Computer Science, Main Campus, IQRA University, Karachi
Tahimna Khan Department of Computer Information Technology, Aligarh Institute of Technology (AIT)
S. M. Ghazanfar Monir Karachi School of Business & Leadership.
Dilbar Hussain Department of Computer Science, Main Campus, IQRA University, Karachi
Rumaisa Iftikhar Department of Electronic Engineering, Sir Syed University of Engineering and Technology, Karachi

Keywords:

Basis Vectors, Signal Processing, Real and Complex Signals, Sequency Domain

Abstract

Independent basis of the linear vectors is of paramount significance in the advancement of digital systems that facilitate the processing and storage of information in its digital format. This study undertakes a thorough examination of discrete orthogonal transformations, with particular focus on the family of real and complex Hadamard transforms and their numerous types. The efficacy of various sequences is scrutinized, alongside their mathematical representation, inherent characteristics, and applications in signal processing. An analysis of the computational cost associated with the complex Hadamard Transform and its variants is presented. Furthermore, simulation outcomes are contrasted for the normalized sequency concerning magnitude response, image compression, and peak signal-to-noise ratio across a variety of image processing applications.

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