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

Independent basis of the linear vectors isof 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 applicationsin 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.