The Ortogonal Property of Directional short-time quaternion Fourier transform

Abstract

This study will examine the orthogonal properties of Directional Short-time quaternion Fourier transform (DSTQFT) which is a further study of DSTFT with an expansion in the form of a function that has a Quaternion value. The orthogonal properties of DSTQFT are obtained by combining the orthogonal properties of  DSTFT and the Fourier quaternion transform (QFT). Based on the results of the study, it was found that the orthogonal nature of the Directional Short-Time quaternion Fourier Transform (DSTQFT) is different from the orthogonal nature of the Directional Short-Time Fourier Transform (DSTFT). In addition, there are three important consequences of orthogonality in TFQSTB as a result of the quaternion-valued function.