Complete analysis of the Eigen functions of Fourier transform

机译：傅立叶变换的本征函数的完整分析

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In this paper, we proposed an analysis of Eigen functions of the n-Dimensional Fourier transform. We extended the theory developed in our previous publication [1]. We applied our extended theory of systematic construction of Eigen function concept for sine and cosine functions. We explained the concept in a clear way through example construction of Eigen functions of 1-D and 2-D Fourier transform for real even case with negative Eigen value. PP Vaidyanathan discussed in his paper [2] that construction of complex Eigen function f1+ jf2 is possible when both functions f1 and f2 are either real even or real odd. But he didn't discuss what will happen when f1 and f2 are different. We subjected this concept and derived the necessary expressions for complex Eigen functions when function f1 is even and function f2 is odd vice versa.

机译：在本文中，我们提出了对n维傅立叶变换的特征函数的分析。我们扩展了先前出版物中发展的理论[1]。我们对正弦和余弦函数应用了本征函数概念的系统构建扩展理论。我们通过示例性构造一维和二维傅立叶变换的本征函数，以清晰的方式解释了该概念，该方法适用于负本征值的实数偶数情况。 PP Vaidyanathan在他的论文中讨论了[2]，当两个函数f 1 和f都可以构造复本征函数f 1 + jf 2 2 是实数偶数或实数奇数。但是他没有讨论f 1 和f 2 不同时会发生什么。当函数f 1 为偶数且函数f 2 为奇数时，我们接受了这一概念并推导了复杂的本征函数的必要表达式。

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来源
《2013 International Conference on Computer Communication and Informatics.》|2013年|p.1-6|共6页
会议地点 Coimbatore(IN);Coimbatore(IN)
作者
Mandru Nagendra Prasad; Bavirisetti Durga Prasad; Karuna Yepuganti; Dhuli Ravindra;
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作者单位

School of Electronics Engineering, VIT University, Vellore, Tamilnadu-632014, India;

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会议组织
原文格式 PDF
正文语种 eng
中图分类计算机网络;计算机网络;
关键词
Eigen function; Eigen value; real even; real odd; sinusoidal;

机译：特征函数;特征值;实数偶数;实数奇数;正弦曲线;;

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1. The numerical method of Fourier eigen transform and its application in seismicity analysis [J] . 陈兵, 郑治真, 江在森地震学报：英文版 . 1997,第006期

机译：傅里叶eIGen变换的数值方法及其在地震性分析中的应用
2. Correlation functions of complete CBOC signals derived as the inverse Fourier transform of energy spectra [J] . Yarlykov M. S., Yarlykova S. M. Journal of Communications Technology and Electronics . 2017,第2期

机译：完整CBOC信号的相关函数作为能谱的傅立叶逆变换
3. Fourier transforms in the “classical sense”, Schur spaces and a new formula for the Fourier transforms of slowly increasing, O(p, q)-invariant functions [J] . Norbert Ortner Indagationes Mathematicae . 2013,第1期

机译：“经典意义”上的傅立叶变换，舒尔空间和缓慢增加的O（p，q）不变函数的傅立叶变换的新公式
4. Complete analysis of The Eigen functions of Fourier Transform [C] . Nagendra Prasad Mandru, Durga Prasad Bavirisetti, Yepuganti Karuna, ICCCI 2013 . 2013

机译：完全分析傅里叶变换的eIGEN函数
5. ENTIRE FUNCTIONS AND FOURIER TRANSFORMS. [D] . GHUSAYNI, BADIH NAJIB. 1986

机译：整个功能和傅里叶变换。
6. Functional Roles of D2-Lys317 and the InteractingChloride Ion in the Water Oxidation Reaction of Photosystem II AsRevealed by Fourier Transform Infrared Analysis [O] . Hiroyuki Suzuki, Jianfeng Yu, Takashi Kobayashi, -1

机译：D2-Lys317的功能作用及其相互作用光系统II As的水氧化反应中的氯离子通过傅立叶变换红外分析揭示
7. (with an Author's Supplement on Monotonic Functions, Stieltjes Integrals and Harmonic Analysis). (Translated from the original 1932 German edition by M. Tenenbaum and H. Pollard.)S.BochnerLectures on Fourier Integrals$5.00Annals of Mathematics Study No. 421959Princeton University PressNew York333(reprinted 1953)S.BochnerK.ChandrasekharanFourier Transforms$3.50Annals of Mathematics Study No. 191948Princeton University Press219$4.50S.BochnerHarmonic Analysis and the Theory of Probability1955University of California Press176 [O] . Mandelbrot Benoit 1960

机译：（以及有关单调函数，Stieltjes积分和调和分析的作者补充）。（由M.Tenenbaum和H.Pollard撰写的1932年德文原版翻译而成）S.Bochner傅里叶积分讲义$ 5.00数学研究年鉴421959普林斯顿大学出版社纽约333（再版1953年）S.Bochner K.ChandrasekharanFourier变换$ 3.50数学研究年鉴$ 3.50 No.191948普林斯顿大学出版社219美元4.50 S.Bochner谐波分析与概率论1955年加利福尼亚大学出版社176
8. TABLES FOR THE NUMERICAL DETERMINATION OF THE FOURIER TRANSFORM OF A FUNCTION OF TIME AND THE INVERSE FOURIER TRANSFORM OF A FUNCTION OF FREQUENCY, WITH SOME APPLICATIONS TO OPERATIONAL CALCULUS METHODS [R] . Carl R. Huss, James J. Donegan 1957

机译：用于数值确定时间函数的傅立叶变换和频率函数的逆傅立叶变换的数字表，以及对运算计算方法的一些应用

Complete analysis of the Eigen functions of Fourier transform

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