Detection of signals with the orthogonal basis of the Gauss–Hermite functions

2018 ◽  
Vol 1 (1) ◽  
pp. 48-61
Author(s):  
D. A. Balakin ◽  
◽  
S. S. Churkin ◽  
V. V. Shtykov ◽  
◽  
...  
Keyword(s):  
Orthogonal Basis ◽  
Hermite Functions ◽  
Detection Of Signals

scholarly journals On bicomplex Fourier–Wigner transforms

2020 ◽  
Vol 18 (03) ◽  
pp. 2050008
Author(s):  
A. El Gourari ◽  
A. Ghanmi ◽  
K. Zine
Keyword(s):  
Orthogonal Basis ◽  
Hermite Functions ◽  
Window Function ◽  
Specific Class ◽  
Wigner Transform ◽  
Basic Properties ◽  
Bicomplex Numbers ◽  
Integrable Functions ◽  
Square Integrable Functions

We consider the [Formula: see text]d and [Formula: see text]d bicomplex analogues of the classical Fourier–Wigner transform. Their basic properties, including Moyal’s identity and characterization of their ranges giving rise to new bicomplex–polyanalytic functional spaces are discussed. Details concerning a special window function are developed explicitly. An orthogonal basis for the space of bicomplex-valued square integrable functions on the bicomplex numbers is constructed by means of a specific class of bicomplex Hermite functions.

Improvements on the gaseous detector device

1986 ◽  
Vol 44 ◽  
pp. 630-631 ◽  
Author(s):  
G.D. Danilatos
Keyword(s):  
Gaseous Medium ◽  
The Other ◽  
Beam Specimen ◽  
Thin Wires ◽  
Interference Noise ◽  
Backscattered Electron ◽  
Detection Of Signals ◽  
Environmental Sem

The possibility of placing the specimen in a gaseous medium in the environmental SEM (ESEM) has created novel ways for detection of signals from the beam-specimen interactions. It was originally reported by Oanilatos that the ionization produced by certain signals inside the conditioning medium can be used to produce images. The aim of this report is to demonstrate some of the improvements on the system that have occurred thereafter.Two straight thin wires are aligned horizontally along a direction normal to the direction of the two scintillator backscattered electron (BSE) detectors reported elsewhere. The free end tips of the wires are about 5 mm apart halfway between the specimen and the pressure limiting aperture (specimen distance = 1.5 mm). The other end of each wire makes contact with the input of a separate preamplifier, two of which are built inside a shielding aluminum stub. With such a design, interference noise from the input cables is avoided.

Detection of Signals in Nongaussian Nonstationary Interference From the Underlying Surface

2016 ◽  
Vol 5 (4) ◽  
pp. 23-39
Author(s):  
V.F. Kravchenko ◽  
◽  
O.V. Kravchenko ◽  
V.I. Lutsenko ◽  
I.V. Lutsenko ◽  
...  
Keyword(s):  
Underlying Surface ◽  
Detection Of Signals

scholarly journals New ideas for handling of loop and angular integrals in D-dimensions in QCD

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Valery E. Lyubovitskij ◽  
Fabian Wunder ◽  
Alexey S. Zhevlakov
Keyword(s):  
Computer Algebra ◽  
Cross Sections ◽  
Orthogonal Basis ◽  
Computer Algebra Systems ◽  
Covariant Formalism ◽  
Linear Combinations ◽  
Recursion Relations ◽  
New Ideas ◽  
Rotational Invariant ◽  
Geometric Picture

Abstract We discuss new ideas for consideration of loop diagrams and angular integrals in D-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of linear combinations of external momenta. It gives a very simple representation for the final results and is more convenient for calculations on computer algebra systems. In case of angular integrals we demonstrate how to simplify the integration of differential cross sections over polar angles. Also we derive the recursion relations, which allow to reduce all occurring angular integrals to a short set of basic scalar integrals. All order ε-expansion is given for all angular integrals with up to two denominators based on the expansion of the basic integrals and using recursion relations. A geometric picture for partial fractioning is developed which provides a new rotational invariant algorithm to reduce the number of denominators.

scholarly journals Efficient experimental quantum fingerprinting with channel multiplexing and simultaneous detection

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Xiaoqing Zhong ◽  
Feihu Xu ◽  
Hoi-Kwong Lo ◽  
Li Qian
Keyword(s):  
Communication Complexity ◽  
Single Photon ◽  
Simultaneous Detection ◽  
Minimum Amount ◽  
Photon Detectors ◽  
Communication Time ◽  
Quantum Communication Complexity ◽  
Detection Of Signals ◽  
Coherent Quantum ◽  
Quantum Fingerprinting

AbstractQuantum communication complexity explores the minimum amount of communication required to achieve certain tasks using quantum states. One representative example is quantum fingerprinting, in which the minimum amount of communication could be exponentially smaller than the classical fingerprinting. Here, we propose a quantum fingerprinting protocol where coherent states and channel multiplexing are used, with simultaneous detection of signals carried by multiple channels. Compared with an existing coherent quantum fingerprinting protocol, our protocol could consistently reduce communication time and the amount of communication by orders of magnitude by increasing the number of channels. Our proposed protocol can even beat the classical limit without using superconducting-nanowire single photon detectors. We also report a proof-of-concept experimental demonstration with six wavelength channels to validate the advantage of our protocol in the amount of communication. The experimental results clearly prove that our protocol not only surpasses the best-known classical protocol, but also remarkably outperforms the existing coherent quantum fingerprinting protocol.

scholarly journals Heisenberg–Weyl Groups and Generalized Hermite Functions

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1060
Author(s):  
Enrico Celeghini ◽  
Manuel Gadella ◽  
Mariano A. del del Olmo
Keyword(s):  
Hilbert Space ◽  
Fourier Transform ◽  
Heisenberg Group ◽  
Real Line ◽  
Hermite Functions ◽  
Unitary Representations ◽  
Weyl Groups ◽  
The Real ◽  
Symmetry Properties ◽  
The Fourier Transform

We introduce a multi-parameter family of bases in the Hilbert space L2(R) that are associated to a set of Hermite functions, which also serve as a basis for L2(R). The Hermite functions are eigenfunctions of the Fourier transform, a property that is, in some sense, shared by these “generalized Hermite functions”. The construction of these new bases is grounded on some symmetry properties of the real line under translations, dilations and reflexions as well as certain properties of the Fourier transform. We show how these generalized Hermite functions are transformed under the unitary representations of a series of groups, including the Weyl–Heisenberg group and some of their extensions.

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