Uncertainty principles associated with the directional short-time Fourier transform
Hatem Mejjaoli, Firdous A. Shah
Abstract
This paper deals with the study of some uncertainty principles associated with the directional short-time Fourier transform. First, we develop the Beckner’s uncertainty principle by invoking the well-known Pitt’s inequality and then study some logarithmic Sobolev-type inequalities. Second, we present a couple of concentration uncertainty principles, including the Benedick–Amrein–Berthier inequality and the local-type uncertainty principle. We culminate our study by formulating the Donoho–Stark-type uncertainty principles for the directional short-time Fourier transform.
Topics & Concepts
Uncertainty principleFourier transformMathematicsLogarithmInequalityType (biology)Discrete Fourier transform (general)Mathematical analysisFourier analysisApplied mathematicsFractional Fourier transformCalculus (dental)PhysicsQuantum mechanicsMedicineBiologyQuantumDentistryEcologyMathematical Analysis and Transform MethodsImage and Signal Denoising MethodsDigital Filter Design and Implementation