The Whittaker-Shannon sampling theorem for experimental reconstruction of free-space wave packets

1997 ◽  
Vol 44 (11-12) ◽  
pp. 2565-2574 ◽  
Author(s):  
M. G. Raymer
Keyword(s):  
Free Space ◽  
Wave Packets ◽  
Sampling Theorem ◽  
Shannon Sampling Theorem ◽  
Space Wave

scholarly journals Nyquist-Shannon sampling theorem applied to refinements of the atomic pair distribution function

2011 ◽  
Vol 84 (13) ◽  
Author(s):  
Christopher L. Farrow ◽  
Margaret Shaw ◽  
Hyunjeong Kim ◽  
Pavol Juhás ◽  
Simon J. L. Billinge
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Sampling Theorem ◽  
Atomic Pair Distribution Function ◽  
Atomic Pair ◽  
Shannon Sampling Theorem

scholarly journals Shannon Wavelets for the Solution of Integrodifferential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Carlo Cattani
Keyword(s):  
Hypergeometric Series ◽  
Sampling Theorem ◽  
Integrodifferential Equations ◽  
Series Connection ◽  
Wavelet Representation ◽  
Connection Coefficients ◽  
Shannon Sampling Theorem ◽  
Shannon Wavelet ◽  
Definition Of ◽  
Shannon Wavelets

Shannon wavelets are used to define a method for the solution of integrodifferential equations. This method is based on (1) the Galerking method, (2) the Shannon wavelet representation, (3) the decorrelation of the generalized Shannon sampling theorem, and (4) the definition of connection coefficients. The Shannon sampling theorem is considered in a more general approach suitable for analysing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction ofL2(ℝ)functions. Shannon wavelets areC∞-functions and their any order derivatives can be analytically defined by some kind of a finite hypergeometric series (connection coefficients).

Determination of the velocity of short electromagnetic waves by interferometry

1952 ◽  
Vol 213 (1112) ◽  
pp. 123-141 ◽  
Keyword(s):  
Phase Velocity ◽  
Electromagnetic Radiation ◽  
Free Space ◽  
Electromagnetic Waves ◽  
Wave Beam ◽  
Wave Length ◽  
Wave Frequency ◽  
Space Wave

A new measurement of the velocity of electromagnetic radiation is described. The result has been obtained, using micro-waves at a frequency of 24005 Mc/s ( λ = 1∙25 cm), with a form of interferometer which enables the free-space wave-length to be evaluated. Since the micro-wave frequency can also be ascertained, phase velocity is calculated from the product of frequency and wave-length. The most important aspect of the experiment is the application to the measured wave-length of a correction which arises from diffraction of the micro-wave beam. This correction is new to interferometry and is discussed in detail. The result obtained for the velocity, reduced to vacuum conditions, is c 0 = 299792∙6 ± 0∙7 km/s.

scholarly journals A note on Whittaker's cardinal series in harmonic analysis

1986 ◽  
Vol 29 (3) ◽  
pp. 349-357 ◽  
Author(s):  
M. M. Dodson ◽  
A. M. Silva ◽  
V. Soucek
Keyword(s):  
Control Theory ◽  
Data Processing ◽  
Harmonic Analysis ◽  
Real Function ◽  
Sampling Theorem ◽  
Communication Engineering ◽  
Shannon Sampling Theorem ◽  
Band Limited ◽  
Image Position ◽  
Sampling Set

The sampling theorem, often referred to as the Shannon or Whittaker-Kotel'nikov- Shannon sampling theorem, is of considerable importance in many fields, including communication engineering, electronics, control theory and data processing, and has appeared frequently in various forms in engineering literature (a comprehensive account of its numerous extensions and applications is given in [3]). The result states that a band-limited signal, i.e. a real function f of the formwhere w>0, is under reasonable conditions on the even function F, determined by its values on the sampling set (l/2w)ℤ and can be reconstructed from the samples f(k/2w), k∈ℤ, by the series

Study on Fault Diagnosis of Gear Transmission which is Based on ADAMS

2012 ◽  
Vol 215-216 ◽  
pp. 812-816
Author(s):  
Shi Ming Wang ◽  
Xian Zhu Ai ◽  
Chao Lv ◽  
Li Na Ma
Keyword(s):  
Time Domain ◽  
Mechanical Energy ◽  
Electric Energy ◽  
Image Data ◽  
Real Data ◽  
Sampling Theorem ◽  
Drive Gear ◽  
Ocean Wave Energy ◽  
Shannon Sampling Theorem ◽  
Simulation Parameters

Introduced a transmission system of a new oscillation buoy ocean wave energy generation device, the system can transform the mechanical energy into electric energy. A pair of gear model was built by SOLIDWORKS, the parameter is just the same as the real data, then imported the model into ADAMS. Under the same simulation parameters, two experiments were done, one engaged without failure, the other engaged with one broken tooth of drive wheels. Calculated TIME and STEPS by Shannon sampling theorem, simulated the marker point’s acceleration of the drive gear, then obtain image data of time domain and frequency domain, after analyzed, found this method has a significant meaning to practice.

scholarly journals On the uncertainty inequality as applied to discrete signals

2006 ◽  
Vol 2006 ◽  
pp. 1-22 ◽  
Author(s):  
Y. V. Venkatesh ◽  
S. Kumar Raja ◽  
G. Vidyasagar
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Sampling Theorem ◽  
Discrete Signals ◽  
Bandlimited Signal ◽  
Time Signals ◽  
Shannon Sampling Theorem ◽  
Heisenberg Uncertainty ◽  
Comparison Of The Results ◽  
Uncertainty Inequality

Given a continuous-time bandlimited signal, the Shannon sampling theorem provides an interpolation scheme forexactly reconstructingit from its discrete samples. We analyze the relationship between concentration (orcompactness) in thetemporal/spectral domainsof the (i) continuous-time and (ii) discrete-time signals. The former is governed by the Heisenberg uncertainty inequality which prescribes a lower bound on the product ofeffectivetemporal and spectral spreads of the signal. On the other hand, the discrete-time counterpart seems to exhibit some strange properties, and this provides motivation for the present paper. We consider the following problem:for a bandlimited signal, can the uncertainty inequality be expressed in terms of the samples, using thestandard definitions of the temporal and spectral spreads of the signal?In contrast with the results of the literature, we present a new approach to solve this problem. We also present a comparison of the results obtained using the proposed definitions with those available in the literature.

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