Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: A Unified Transform for LTI Systems—Presented as a (Generalized) Frame | Hindawi Publishing Corporation EURASIP Journal on Applied Signal Processing Volume 2006 Article ID 91604 Pages 1-9 DOI ASP 2006 91604 A Unified Transform for LTI Systems Presented as a Generalized Frame Arie Feuer 1 Paul M. J. Van den Hof 2 and Peter S. C. Heuberger2 1 Department of Electrical Engineering Technion-Israel Institute of Technology Haifa 32000 Israel 2 Delft Center for Systems and Control Delft University of Technology 2628 Delft the Netherlands Received 19 August 2004 Revised 30 May 2005 Accepted 31 May 2005 We present a set of functions in L2 0 oo and show it to be a tight generalized frame as presented by G. Kaiser 1994 . The analysis side of the frame operation is called the continuous unified transform. We show that some of the well-known transforms such as Laplace Laguerre Kautz and Hambo result by creating different sampling patterns in the transform domain or equivalently choosing a number of subsets of the original frame . Some of these resulting sets turn out to be generalized tight frames as well. The work reported here enhances the understanding of the interrelationships between the above-mentioned transforms. Furthermore the impulse response of every stable finite-dimensional LTI system has a finite representation using the frame we introduce here with obvious benefits in identification problems. Copyright 2006 Hindawi Publishing Corporation. All rights reserved. 1. INTRODUCTION Linear time invariant LTI systems representations have been subject of research for many years resulting in a vast amount of literature. Tools such as frequency response FR Laplace transform LP Laguerre bases and Hambo bases see . 2 and references therein play key roles in these investigations. In almost parallel the signal processing community has been developing tools for signal representation such as Fourier transform FT short-time FT STFT continuous wavelet transform CWT and frames see . 35 . We present here an initial effort on our part to find .
