Measures of spread for periodic distributions and the associated uncertainty relations

Keywords

Physics, Fourier series, Fourier transform, Uncertainty principle, Centroid

References

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• Resolution in time-frequencyVictor DeBrunner, Murad Özaydın, Tomasz Przebinda — 1999
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• Prolate spheroidal wave functions, fourier analysis, and uncertainty — V: the discrete caseD. Slepian — 1978
• Proposed international standard for laser-beam quality falls shortG. Lawrence — 1994
• M2 concept characterizes beam qualityT. Johnston — 1990

Cited by

• Mapping-based uncertainty relations for periodic functionsM.J. Bastiaans, Miguel A. Alonso — 2003
• Nonparaxial fields with maximum joint spatial-directional localization. I. Scalar case.Miguel A. Alonso, Riccardo Borghi, Massimo Santarsiero — 2006
• Finite two-dimensional oscillator: II. The radial modelNatig M. Atakishiyev, G. S. Pogosyan, Luis Edgar Vicent — 2001
• On the position uncertainty measure on the circleD. A. Trifonov — 2003
• Minimum uncertainty solutions for partially coherent fields and quantum mixed statesMiguel A. Alonso, Tero Setälä, Ari T. Friberg — 2014
• Uncertainty relations and minimum uncertainty states for the discrete Fourier transform and the Fourier seriesG. W. Forbes, Miguel A. Alonso, A. E. Siegman — 2003
• Uniform estimation of orientation using local and nonlocal 2-D energy operators.Kieran G. Larkin — 2005
• A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns.Kieran G. Larkin — 2001
• Quantization of the canonically conjugate pair angle and orbital angular momentumH.A. Kastrup — 2005
• Quantum diffusion on a cyclic one-dimensional lattice.Alicia Torre, H. O. Mártin, Dardo Goyeneche — 2003
• Consistent analogs of the Fourier uncertainty relationG. W. Forbes, Miguel A. Alonso — 2001
• Direct Magnetic Field Estimation Based on Echo Planar Raw DataFrederik Testud, Daniel Nicolas Splitthoff, Oliver Speck — 2010
• The effect of orbital angular momentum and helicity in the uncertainty-type relations between focal spot size and angular spreadMiguel A. Alonso — 2011
• Experimental test of uncertainty relations for quantum mechanics on a circleJ. Řeháček, Zdeněk Bouchal, Radek Čelechovský — 2007
• Linear transformations and aberrations in continuous and finite systemsKurt Bernardo Wolf — 2008
• Geometry and dynamics in the fractional discrete Fourier transform.Kurt Bernardo Wolf, Guillermo Krötzsch — 2007
• Orbital angular momentum: origins, behavior and applicationsAlison M. Yao, Miles J. Padgett — 2011
• The rigged Hilbert space of the algebra of the one-dimensional rectangular barrier potentialRafael de la Madrid — 2004
• Improved tomographic imaging of wavelength scanning digital holographic microscopy by use of digital spectral shaping.Lingfeng Yu, Zhongping Chen — 2007
• Mapping-based width measures and uncertainty relations for periodic functionsMiguel A. Alonso, Martin J. Bastiaans — 2004

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