A new method to generate superoscillating functions and supershifts
Yakir Aharonov, Fabrizio Colombo, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen
2021Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences24 citationsDOIOpen Access PDF
Abstract
Superoscillations are band-limited functions that can oscillate faster than their fastest Fourier component. These functions (or sequences) appear in weak values in quantum mechanics and in many fields of science and technology such as optics, signal processing and antenna theory. In this paper, we introduce a new method to generate superoscillatory functions that allows us to construct explicitly a very large class of superoscillatory functions.
Topics & Concepts
Construct (python library)Class (philosophy)Fourier transformComputer scienceSignal processingAlgebra over a fieldMathematicsAlgorithmQuantumAntenna (radio)Function (biology)Theoretical computer scienceApplied mathematicsSIGNAL (programming language)Fourier analysisGeneralized functionMultidimensional signal processingMathematical analysisPure mathematicsAnalytic functionCoding theory and cryptographyMathematical Analysis and Transform MethodsDigital Filter Design and Implementation