Tighter Heisenberg–Weyl type uncertainty principle associated with quaternion wavelet transform

Abstract

In this paper, some tighter Heisenberg–Weyl type uncertainty principles for the two-dimensional continuous quaternion wavelet transform (CQWT) was considered by way of a polar coordinate form of the quaternion-valued function. As main consequences, we obtain tighter Heisenberg–Weyl uncertainty principle (UP) for the CQWT in spatial and directional settings respectively, tighter concentration Heisenberg–Weyl UP with the concentration for the CQWT in position and scale, as well as tighter local-type Heisenberg–Weyl UP for the CQWT.