Tighter uncertainty principles associated with Bendlet and quaternion-Bendlet transforms

This paper is devoted to the investigation of several tighter uncertainty principles (UPs) for the continuous Bendlet transform (CBT) and continuous quaternion Bendlet transform (CQBT), respectively, by using the coordinate form for both complex and quaternion signals. We mainly focus on the tighter Heisenberg–Weyl UPs in spatial and directional settings for the CBT and CQBT. Remarkably, these new UPs possess more stringent lower bounds by comparing with the classical UPs.