Fourier transform of bicomplex-valued hyperbolic norm integrable functions

Abstract

For the purpose of this investigation, the Fourier transforms of hyperbolic norm integrable functions with bicomplex values that are constructed on locally compact abelian groups are utilized. Performing an analysis of these transformations is the purpose of this study. The bicomplex-valued Fourier transform is referred to as the $\mathbb{B}\mathbb{C}$-Fourier transform as a result of the nomenclature it utilizes. It is well defined and unique. There is a relationship between this transform and the convolution operator.  The translation and character operators are sometimes included in this transform, which results in outcomes that are comparable to those of the well-known Fourier transform. Many fields employ the Fourier transform to convert a time-dependent function to a frequency-dependent function for time-frequency analysis, including signal processing. Using complex-valued signals is more convenient here. Thus, the $\mathbb{B}\mathbb{C}$-Fourier transform for time-frequency analysis of signals with bicomplex values would be more efficient since bicomplex numbers constitute an extended form of ordinary complex numbers.