Analysis of linear time-varying systems in wavelet domain

Analysis of linear time-varying systems is one of the important problems inengineering. In many solution methods there are some approximations such that the system ismodeled as time-invariant system and/or the solution is obtained in steady-state conditionswithout considering the transient response. The problem is to get a general analysis methodfor LTV systems is still continuing to investigate.In this thesis, time-varying systems are analyzed in wavelet domain. The system equations aredescribed in a higher order differential equation or state-space representation. To solve theseequations, they are transferred to wavelet domain by forming algebraic matrix-vector relationsusing the wavelet transform coefficients. These relations are achieved by defining operatormatrices concerned with addition-subtraction, multiplication, derivative and integral operatorsappear in system equations. Orthogonal and compact support wavelets provide a simple wayto define these operator matrices. The operator matrices have been defined for orthogonalcompactly supported wavelets. Linear time-varying system?s dynamic equations areexpressed as into algebraic matrix-vector relations by using the operator matrices. Inapplication, firstly, system analysis in wavelet domain method is theoretically applied todifferential equation and state-space representation of LTV systems and then some illustrativeexamples are given. Their results are discussed in conclusion.This thesis consists of a literature survey on the linear time-varying systems and their solutiontechniques, the theoretical background of wavelets and wavelets transform, the operationalmatrices of time domain operators and LTV system analysis with wavelets.Key Words: Wavelet domain system analysis, Wavelet transform, Linear time-varyingsystems, Linear operators.