Spectrum of quaternion signals associated with quaternion linear canonical transform

In recent years quaternion linear canonical transform (QLCT) has emerged due to its applications in various fields, including image and signal processing. This article discusses two spectrum-related theorems (real Paley-Wiener and Boas type). The real Paley-Wiener type theorem is formulated to describe the character of a compactly supported two-sided quaternion linear canonical transformed (QLCT) signal. The Boas -type theorem is also discussed to explain the property of right-sided QLCT of signals that vanish in the neighborhood of origin. Some potential applications of these theorems on some particular quaternion -type operators are also discussed.