國立臺灣大學電機工程學系暨研究所貝蘇章2006-07-252018-07-062006-07-252018-07-062005-07-31http://ntur.lib.ntu.edu.tw//handle/246246/8038本研究提出一新穎近似三行對角交換矩陣(Nearly Tridiagonal Commuting Matrices)， 其埃根向量更能逼近類比赫曼 高斯函數(Hermite-Gaussian Functions)，可以應用到數位式離 散分數傅立葉轉換及其應用(Discrete Fractional Fourier Transform) 。Based on discrete Hermite-Gaussian like functions, a discrete fractional Fourier transform (DFRFT) which provides sample approximations of the continuous fractional Fourier transform was defined and investigated recently. In this paper, we propose a new nearly tridiagonal matrix which commutes with the discrete Fourier transform (DFT) matrix. The eigenvectors of the new nearly tridiagonal matrix are shown to be better discrete Hermite-Gaussian like functions than those developed before. Furthermore, by appropriately combining two linearly independent matrices which both commute with the DFT matrix, we develop a method to obtain even better discrete Hermite-Gaussian like functions. Then, new versions of DFRFT produce their transform outputs more close to the samples of the continuous fractional Fourier transform, and their application is illustrated.application/pdf119089 bytesapplication/pdfzh-TW國立臺灣大學電機工程學系暨研究所reporthttp://ntur.lib.ntu.edu.tw/bitstream/246246/8038/1/932213E002059.pdf