FORMULATION OF THE CORRELATION ON THE REDUCED LINEAR BIQUATERNION CANONIC TRANSFORMATION

This research aims to formulate a correlation theorem on the canonical transformation of reduced linear biquaternion (RBLCT).This research is a literature review conducted at the Department of Industrial Technology, Makassar PSDKU Graphics Engineering Study Programme, Politeknik Negeri Media Kreatif.The definition of reduced biquaternion linear canonical transformation (RBLCT) is obtained by first constructing the definition of reduced biquaternion Fourier transform (FTRB) and investigating its properties by replacing the kernel of Fourier Transform with the kernel of FTRB in the definition of Linear Canonical Transformation (LCT). The proposed Correlation Theorem for RBLCT is an extension of the correlation theorem of linear canonical transform to the domain of RBLCT. A different proof of the Parseval formula for RBLCT is also given whose proof is much simpler by using the conjugacy property of the RBLCT kernel. As an application of the obtained results, the RBLCT correlation theorem is briefly discussed to study frequency-swift filters in general.