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The Quaternion Domain Fourier Transform and its Application in Mathematical Statistics Mawardi Bahri, Amir Kamal Amir, Resnawati, and Chrisandi Lande Abstract—Recently a generalization of the quaternion Fourier transform over quaternion domains so-called the quaternion domain Fourier transform (QDFT) has been in- troduced, including its properties such as shift, modulation, convolution theorem and uncertainty principle. In the present paper we explore more properties of the QDFT such as the correlation and product theorems and propose its application in probability theory and mathematical statistics. Index Terms—quaternion domain Fourier transform, quater- nion random variable I. INTRODUCTION It is well known that in signal and image processing, the
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