Sonlu faz uzayında harmonik analiz

ABSTRACTHARMONIC ANALYSIS INFINITE PHASE SPACESayit KorkmazM.S. in Electrical and Electronics EngineeringüSupervisor: Prof. Dr. Haldun M. Ozaktaş sAugust 2005The Wigner distribution and linear canonical transforms are important tools foroptics, signal processing, quantum mechanics, and mathematics. In this thesis, westudy the discrete versions of Wigner distributions and linear canonical transforms.In the definition of a discrete entity we focus on two aspects: structural analogy andcontinuum approximation and/or limits. Based on this framework, the tradeoffsare analyzed and a compromise for a discrete Wigner distribution that meets bothobjectives to a high degree is presented by consolidating sampling theory and the al-gebraic approach. Such a compromise is necessary since it is impossible to meet theconditions to the highest possible degree. The differences between discrete and con-tinuous time-frequency analysis are also discussed in a group theoretical perspective.In the second part of the thesis, the discrete versions of linear canonical transformsare reviewed and their connections to the continuous theory is established. As aspecial case the discrete fractional Fourier transform is defined and its propertiesare derived.Keywords: discrete Wigner distributions, discrete time-frequency analysis, discretelinear canonical transforms, discrete fractional Fourier transform.iii