scholarly journals A new method to generate superoscillating functions and supershifts

2021 ◽  
Vol 477 (2249) ◽  
pp. 20210020
Author(s):  
Yakir Aharonov ◽  
Fabrizio Colombo ◽  
Irene Sabadini ◽  
Tomer Shushi ◽  
Daniele C. Struppa ◽  
...  
Keyword(s):  
Signal Processing ◽  
Quantum Mechanics ◽  
Large Class ◽  
Science And Technology ◽  
Fourier Component ◽  
New Method ◽  
Weak Values ◽  
Antenna Theory ◽  
Superoscillating Functions ◽  
Band Limited

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.

scholarly journals Holomorphic functions, relativistic sum, Blaschke products and superoscillations

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Daniel Alpay ◽  
Fabrizio Colombo ◽  
Stefano Pinton ◽  
Irene Sabadini
Keyword(s):  
Infinite Order ◽  
Complex Analysis ◽  
Differential Operators ◽  
Entire Functions ◽  
Growth Conditions ◽  
Weak Values ◽  
Blaschke Products ◽  
Independent Field ◽  
Superoscillating Functions ◽  
Band Limited

AbstractSuperoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. The notion of superoscillation is a particular case of that one of supershift. In the recent years, superoscillating functions, that appear for example in weak values in quantum mechanics, have become an interesting and independent field of research in complex analysis and in the theory of infinite order differential operators. The aim of this paper is to study some infinite order differential operators acting on entire functions which naturally arise in the study of superoscillating functions. Such operators are of particular interest because they are associated with the relativistic sum of the velocities and with the Blaschke products. To show that some sequences of functions preserve the superoscillatory behavior it is of crucial importance to prove that their associated infinite order differential operators act continuously on some spaces of entire functions with growth conditions.

Method of estimation of hidden correlation of narrowband noise signals

2019 ◽  
pp. 34-39 ◽  
Author(s):  
E.I. Chernov ◽  
N.E. Sobolev ◽  
A.A. Bondarchuk ◽  
L.E. Aristarhova
Keyword(s):  
Signal Processing ◽  
Digital Signal Processing ◽  
New Technology ◽  
Digital Signal ◽  
Measuring Instruments ◽  
Central Frequency ◽  
Pearson Criterion ◽  
Useful Signal ◽  
Band Limited ◽  
Narrowband Noise

The concept of hidden correlation of noise signals is introduced. The existence of a hidden correlation between narrowband noise signals isolated simultaneously from broadband band-limited noise is theoretically proved. A method for estimating the latent correlation of narrowband noise signals has been developed and experimentally investigated. As a result of the experiment, where a time frag ent of band-limited noise, the basis of which is shot noise, is used as the studied signal, it is established: when applying the Pearson criterion, there is practically no correlation between the signal at the Central frequency and the sum of signals at mirror frequencies; when applying the proposed method for the analysis of the same signals, a strong hidden correlation is found. The proposed method is useful for researchers, engineers and metrologists engaged in digital signal processing, as well as developers of measuring instruments using a new technology for isolating a useful signal from noise – the method of mirror noise images.

INVARIANT EIGEN-OPERATOR METHOD OF DERIVING ENERGY-LEVEL GAP FOR NONCOMMUTATIVE QUANTUM MECHANICS

2005 ◽  
Vol 20 (09) ◽  
pp. 691-698 ◽  
Author(s):  
SI-CONG JING ◽  
HONG-YI FAN
Keyword(s):  
Quantum Mechanics ◽  
Energy Level ◽  
Operator Method ◽  
Simple Algebra ◽  
New Method ◽  
Noncommutative Quantum Mechanics ◽  
Noncommutative Quantum

We propose a new method to derive energy-level gap for Hamiltonians in the context of noncommutative quantum mechanics (NCQM). This method relies on finding invariant eigen-operators whose commutators with Hamiltonian are still the operators themselves but with some eigenvalue-like coefficients, which correspond to the energy-level gaps of the systems. Based on this method, only after some simple algebra, we derive the energy-level gaps for several important systems in NCQM, and most of these results have not been reported in literature so far.

Signal processing in SPR fiber sensors: Some remarks and a new method

2018 ◽  
Vol 268 ◽  
pp. 150-156 ◽  
Author(s):  
E. Rodríguez-Schwendtner ◽  
A. González-Cano ◽  
N. Díaz-Herrera ◽  
M.C. Navarrete ◽  
Ó. Esteban
Keyword(s):  
Signal Processing ◽  
New Method ◽  
Fiber Sensors

scholarly journals A New Method of Mass Measurement for Checkweighers

2010 ◽  
Vol 17 (2) ◽  
pp. 151-162 ◽  
Author(s):  
Kengo Fukuda ◽  
Koji Yoshida ◽  
Tetsuya Kinugasa ◽  
Morihito Kamon ◽  
Yoichiro Kagawa ◽  
...  
Keyword(s):  
Signal Processing ◽  
Production Process ◽  
Mass Measurement ◽  
Automatic Machine ◽  
New Method ◽  
Time Duration ◽  
Optical Device

A New Method of Mass Measurement for CheckweighersA checkweigher is an automatic machine to measure the weight of in-motion products. It is usually located around the end of the production process and ensures the weight of a product within specified limits. Any products are taken out of line if their weights are out of the specified limits. It is usually equipped with an optical device. It is used to make a trigger to set the time duration to allow a product to move completely on the weigh belt for sampling the weight. In this paper, a new method of mass measurement for checkweighers is proposed which uses just signal processing without the optical device. The effectiveness of the method is shown through experiments. Also a possibility of faster estimation of weight is shown.

LIE-ALGEBRAIC APPROACH TO THE PROBLEM OF QUASI-EXACT SOLUBILITY IN QUANTUM MECHANICS

1990 ◽  
Vol 05 (23) ◽  
pp. 1891-1899 ◽  
Author(s):  
A. G. USHVERIDZE
Keyword(s):  
Quantum Mechanics ◽  
Lie Algebras ◽  
Algebraic Approach ◽  
New Method ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Simple Lie Algebras ◽  
Infinite Dimensional ◽  
Exactly Solvable

A new method of constructing quasi-exactly solvable models of quantum mechanics is proposed. This method is based on the use of infinite-dimensional representations of simple and semi-simple Lie algebras.

GENERATING SHAPE INVARIANT POTENTIALS

2008 ◽  
Vol 23 (31) ◽  
pp. 4959-4978 ◽  
Author(s):  
ASIM GANGOPADHYAYA ◽  
JEFFRY V. MALLOW
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics ◽  
New Method ◽  
Invariance Condition ◽  
Partial Differential ◽  
Shape Invariance ◽  
Shape Invariant

We transform the shape invariance condition, a difference-differential equation of supersymmetric quantum mechanics, into a local partial differential equation. We develop a new method for generating translationally shape invariant potentials from this equation. We generate precisely all the known shape invariant potentials, and argue that there are unlikely to be others.

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