The N-Dimensional Uncertainty Principle for the Free Metaplectic Transformation
Rui Jing, Bei Liu, Rui Li, Rui Liu
Abstract
The free metaplectic transformation is an N-dimensional linear canonical transformation. This transformation operator is useful, especially for signal processing applications. In this paper, in order to characterize simultaneously local analysis of a function (or signal) and its free metaplectic transformation, we extend some different uncertainty principles (UP) from quantum mechanics including Classical Heisenberg’s uncertainty principle, Nazarov’s UP, Donoho and Stark’s UP, Hardy’s UP, Beurling’s UP, Logarithmic UP, and Entropic UP, which have already been well studied in the Fourier transform domain.
Topics & Concepts
Uncertainty principleTransformation (genetics)Fourier transformLogarithmLinear mapCanonical transformationMathematicsDomain (mathematical analysis)SIGNAL (programming language)Operator (biology)Pure mathematicsQuantumMathematical analysisPhysicsQuantum mechanicsComputer scienceProgramming languageRepressorGeneBiochemistryTranscription factorChemistryMathematical Analysis and Transform MethodsImage and Signal Denoising MethodsDigital Filter Design and Implementation