Uncertainty relations for signal concentrations associated with the linear canonical transform

Uncertainty principles associated with quaternion linear canonical transform and their estimates

“…Proposition 3.10 (Sharp Young-Hausdorff inequality for 2D LCT). Let p ∈ [1,2] and q be such that 1 p + 1 q = 1, then…”

“…As the inequalities of LCT are much more explored than the inequalities of QLCT, so we can easily discuss many other inequalities of the QLCT by using the OPS method, which may be applicable to the right‐sided QLCT domain. Uncertainty principles (UPs) have many real‐world applications; namely, Xu et al 1 proposed the uncertainty principle for signal concentrations in the LCT domain. It is useful to find an input signal, which its energy is specified to maximize the energy of the output signal of the linear system in signal processing.…”

“…The uncertainty principles play a major role in the growth of the theory of optics, signal processing, 1,2 applied physics, 3 and so forth. First, it was formulated by the German physicist Heisenberg 4 .…”