Related papers: Sensitivity of Yield Optimized Superoscillations
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…
In the last decade there has been a growing interest in superoscillations in various fields of mathematics, physics and engineering. However, while in applications as optics the local oscillatory behaviour is the important property, some…
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…
A remarkable phenomenon of superoscillations implies that electromagnetic waves can locally oscillate in space or time faster than the fastest spatial and temporal Fourier component of the entire function. This phenomenon allows to focus…
We construct a signal from "almost" pure oscillations within some low frequency band. We construct it to produce a superoscillation with frequency above the nominal band limit. We find that indeed the required high frequency is produced but…
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…
One of the fundamental problems in communications is finding the energy distribution of signals in time and frequency domains. It should, therefore, be of great interest to find the most energy concentration hypercomplex signal. The present…
Quantitative helio- and asteroseismology require very precise measurements of the frequencies, amplitudes, and lifetimes of the global modes of stellar oscillation. It is common knowledge that the precision of these measurements depends on…
Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may…
Superoscillation (SO) wavefunctions, that locally oscillate much faster than its fastest Fourier component, in light waves have enhanced optical technologies beyond diffraction limits, but never been controlled into 2D periodic lattices.…
In the sciences and engineering, the concept of bandwidth is often subject to interpretation depending upon context and the requirements of a specific community. The focus of this work is to formulate this concept for a general class of…
Spectrum sensing is a fundamental operation in cognitive radio environment. It gives information about spectrum availability by scanning the bands. Usually a fixed amount of time is given to scan individual bands. Most of the times,…
The Fourier theorem states that any time-series can be decomposed into a set of sinusoidal frequencies, each with its own phase and amplitude. The literature suggests that some frequencies are important to reproduce key qualities of…
We study an aspect of the following general question: which properties of a signal can be characterized by its scattering transform? We show that the energy contained in high order scattering coefficients is upper bounded by the energy…
A definition of frequency (cycles per unit-time) based on an approximate reconstruction of the phase-space trajectory of an oscillator from a signal is introduced. It is shown to be invariant under linear filtering, and therefore…
Functions that are smooth but non-periodic on a certain interval possess Fourier series that lack uniform convergence and suffer from the Gibbs phenomenon. However, they can be represented accurately by a Fourier series that is periodic on…
This paper proposes a novel, rigorous and simple Fourier-transformation approach to study resonances in a perfectly conducting slab with finite number of subwavelength slits of width $h\ll 1$. Since regions outside the slits are variable…
We study the problem of interpolating a noisy Fourier-sparse signal in the time duration $[0, T]$ from noisy samples in the same range, where the ground truth signal can be any $k$-Fourier-sparse signal with band-limit $[-F, F]$. Our main…
Oscillators have two main limitations: their synchronization properties are limited (i.e they have a finite synchronization region) and they have no memory of past interactions (i.e. they return to their intrinsic frequency whenever the…
Frequency estimation from measurements corrupted by noise is a fundamental challenge across numerous engineering and scientific fields. Among the pivotal factors shaping the resolution capacity of any frequency estimation technique are…