Related papers: Yield--Optimized Superoscillations
Super oscillating signals are band limited signals that oscillate in some region faster than their largest Fourier component. Such signals have many obvious scientific and technological applications, yet their practical use is strongly…
The phenomenon of superoscillation, where band limited signals can oscillate over some time period with a frequency higher than the band limit, is not only very interesting but it also seems to offer many practical applications. The first…
Yield Optimized Interpolated Superoscillations (YOIS) have been recently introduced as a means for possibly making the use of the phenomenon of superoscillation practical. In this paper we study how good is a superoscillation that is not…
Superoscillatory wave forms, i.e., waves that locally oscillate faster than their highest Fourier component, possess unusual properties that make them of great interest from quantum mechanics to signal processing. However, the more…
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…
A function f is said to possess superoscillations if, in a finite region, f oscillates faster than the shortest wavelength that occurs in the Fourier transform of f. I will discuss four aspects of superoscillations: 1. Superoscillations can…
Surprisingly, differentiable functions are able to oscillate arbitrarily faster than their highest Fourier component would suggest. The phenomenon is called superoscillation. Recently, a practical method for calculating superoscillatory…
In ordinary circumstances the highest frequency present in a wave is the highest frequency in its Fourier decomposition. It is however possible for there to be a spatial or temporal region of the wave which locally oscillates at a still…
Waves are superoscillatory where their local phase gradient exceeds the maximum wavenumber in their Fourier spectrum. We consider the superoscillatory area fraction of random optical speckle patterns. This follows from the joint probability…
Superoscillations, i.e., the phenomenon that a bandlimited function can temporary oscillate faster than its highest Fourier component, are being much discussed for their potential for `superresolution' beyond the diffraction limit. Here, we…
Superoscillations occur when a globally band-limited function locally oscillates faster than its highest Fourier coefficient. We generalize this effect to arbitrary quantum mechanical operators as a weak value, where the preselected state…
Superoscillations have roots in various scientific disciplines, including optics, signal processing, radar theory, and quantum mechanics. This intriguing mathematical phenomenon permits specific functions to oscillate at a rate surpassing…
Superoscillating functions, i.e., functions that locally oscillate at a rate faster than their highest Fourier component, are of interest for applications from fundamental physics to engineering. Here, we develop a new method which allows…
Supergrowth refers to the local amplitude growth rate of a signal being faster than its fastest Fourier mode. In contrast, superoscillation pertains to the variation of the phase. Compared to the latter, supergrowth can have exponentially…
Super-resolution is the problem of recovering a superposition of point sources using bandlimited measurements, which may be corrupted with noise. This signal processing problem arises in numerous imaging problems, ranging from astronomy to…
Band-limited functions can oscillate locally at an arbitrarily fast rate through an interference phenomenon known as superoscillations. Using an optical pulse with a superoscillatory envelope we experimentally break the temporal…
Arguments from scale physics, augmented by numerical and analytical investigations, are used to consider the probability and the detectability of superoscillations in generic functions. The detectability is defined as the fraction of the…
Superoscillations are a phenomenon where a band-limited wave may locally oscillate faster than its highest Fourier component. They are a product of destructive interference between the wave's constituent harmonics. In this article, we…
Oscillatory systems arise in the different science fields. Complex mathematical formulations with differential equations have been proposed to model the dynamics of these systems. While they have the advantage of having a direct…
It has been found that functions can oscillate locally much faster than their Fourier transform would suggest is possible - a phenomenon called superoscillation. Here, we consider the case of superoscillating wave functions in quantum…