The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform

Barker L.; Hakioglu T.; Kutay MA.; Ozaktas HM.; Candan C.

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The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform

机译：离散谐波振荡器，Harper方程和离散分数阶傅里叶变换

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Certain solutions to Harper's equation are discrete analogues of (and approximations to) the Hermite-Gaussian functions. They are the energy eigenfunctions of a-discrete algebraic analogue of the harmonic oscillator, and they lead to a definition of a discrete fractional Fourier transform (FT). The discrete fractional FT is essentially the time-evolution operator of the discrete harmonic oscillator. [References: 35]

机译：Harper方程的某些解决方案是Hermite-Gaussian函数的离散近似（和近似）。它们是谐波振荡器的a离散代数模拟的能量本征函数，它们导致了离散分数阶Fourier变换（FT）的定义。离散分数FT本质上是离散谐波振荡器的时间演化算子。 [参考：35]

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《Journal of Physics, A. Mathematical and General: A Europhysics Journal》 |2000年第11期|共14页
作者
Barker L.; Hakioglu T.; Kutay MA.; Ozaktas HM.; Candan C.;
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正文语种 eng
中图分类物理学;
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Quantum-mechanics; Wigner-function;

机译：量子力学;维格纳函数;

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专利

1. The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform [J] . Barker L., Hakioglu T., Kutay MA., Journal of Physics, A. Mathematical and General: A Europhysics Journal . 2000,第11期

机译：离散谐波振荡器，Harper方程和离散分数阶傅里叶变换
2. High Security Multiple-image Encryption using Discrete Cosine Transform and Discrete Multiple-Parameter Fractional Fourier Transform [J] . Guanghui Ren, Jianan Han, Haihui Zhu, Journal of Communications . 2016,第5期

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3. Optimal Joint Design of Discrete Fractional Fourier Transform Matrices and Mask Coefficients for Multichannel Filtering in Fractional Fourier Domains [J] . Xiao-Zhi Zhang, Bingo Wing-Kuen Ling, Hai Huyen Dam, IEEE Transactions on Signal Processing . 2018,第22期

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4. DISCRETE-TO-DISCRETE PROLATE SPHEROIDAL WAVE FUNCTIONSAND FINITE DURATION DISCRETE FRACTIONAL FOURIER TRANSFORM [C] . Soo-Chang Pei, Jian-Jiun Ding EUSIPCO 2007;European signal processing conference . 2007

机译：离散到离散的椭球面波函数和有限时间离散分数傅里叶变换
5. The centered discrete fractional Fourier transform, properties, computation, and application to linear chirp signals. [D] . Vargas-Rubio, Juan Gaspar. 2004

机译：中心离散傅里叶分数阶变换，性质，计算以及对线性线性调频信号的应用。
6. Discrete Fourier Transform Radar in the Terahertz-Wave Range Based on a Resonant-Tunneling-Diode Oscillator [O] . Hiroki Konno, Adrian Dobroiu, Safumi Suzuki, 2021

机译：基于谐振隧道二极管振荡器的太赫兹波范围中的离散傅里叶变换雷达
7. The discrete harmonic oscillator, Harper’s equation, and the discrete fractional Fourier transform [O] . Laurence Barker, M Alper Kutay, Haldun M Ozaktas 2000

机译：离散谐振子，Harper方程和离散分数傅里叶变换
8. Comparison of Arithmetic Requirements for the PFA (Prime Factor Algorithm), WFTA (Winograd Fourier Transform Algorithm), SWIFT, MFFT (Mixed Radix Fast Fourier Transform), FFT (Fast Fourier Transform) and DFT (Discrete Fourier Transform) Algorithms. [R] . Hicks, R. C. 1982

机译：pFa（素因子算法），WFTa（Winograd傅立叶变换算法），sWIFT，mFFT（混合基线快速傅里叶变换），FFT（快速傅立叶变换）和DFT（离散傅立叶变换）算法的算术要求的比较。

The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform

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