Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2010 Article ID 191085 7 pages doi 2010 191085 Research Article Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform Ahmet Serbes and Lutfiye Durak-Ata EURASIP Member Department of Electronics and Communications Engineering Yildiz Technical University Yildiz Besiktas 34349 Istanbul Turkey Correspondence should be addressed to Ahmet Serbes Received 19 February 2010 Accepted 24 June 2010 Academic Editor L. F. Chaparro Copyright 2010 A. Serbes and L. Durak-Ata. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Determining orthonormal eigenvectors of the DFT matrix which is closer to the samples of Hermite-Gaussian functions is crucial in the definition of the discrete fractional Fourier transform. In this work we disclose eigenvectors of the DFT matrix inspired by the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As ju in the analog s-domain is mapped to the unit circle one-to-one without aliasing in the discrete z-domain it is appropriate to use it in the discretization of the eigenfunctions of the Fourier transform. We obtain Hermite-Gaussian-like eigenvectors of the DFT matrix. For this purpose we propose three different methods and analyze their stability conditions. These methods include better conditioned commuting matrices and higher order methods. We confirm the results with extensive simulations. 1. Introduction Discretization of the fractional Fourier transform FrFT is vital in many application areas including signal and image processing filtering sampling and time-frequency analysis 1-3 . As FrFT is related to the Wigner distribution 1 it is a powerful tool for time-frequency analysis for example
