On the class of uncertainty inequalities for the coupled fractional Fourier transform

Abstract The coupled fractional Fourier transform $\mathcal {F}_{\alpha ,\beta}$ Fα,β is a two-dimensional depending on two angles α and β , which are in such way that the parameters $\gamma =(\alpha +\beta )/2$ xmlns:mml="http://www.w3.org/1998/Math/MathML">γ=(α+β)/2 $\delta -\beta xmlns:mml="http://www.w3.org/1998/Math/MathML">δ=(α−β)/2 . It generalizes serves as prominent tool some applications of signal image processing. In this article, we formulate new class uncertainty inequalities for (CFrFT). Firstly, establish sharp Heisenberg-type inequality CFrFT then logarithmic local-type inequalities. sequel, several concentration-based inequalities, including Nazarov, Amrein–Berthier–Benedicks, Donoho–Stark’s Towards end, Hardy’s Beurling’s CFrFT.