Online processing of signals has particular importance in control systems. Because these signals have information about system and its performance. Therefore, the accurate description of features of system is possible by extracting the information of signals. Many researches have done on predictable signals in recent years. One group of these signals is exponentially damped sinusoidal (EDS) signals. The EDS signals have many practical applications such as speech/audio analysis, linear system identification and transient analysis. The parameters estimation of the EDS signals consists of the amplitude, frequency, damping factor and phase of the signal. Various methods have been proposed to estimate the parameters of an EDS signal. Some of well-known approaches include matrix pencil method, maximum likelihood method and linear prediction methods. These methods are not suitable for tracking time varying parameters. Therefore, researches have been focused on applying on-line estimators such as Adaline neural networks to track time varying frequency and damping factor. In this thesis, two algorithms based on the Adaline networks are presented for online estimation of the frequency and damping factor of a complex EDS signal. In both algorithms, the unknown parameters of signal put in the weight coefficients of the Adaline networks. The normalized variable step size LMS algorithm is used for training the weights. Furthermore, the proposed methods are extended for a complex biased EDS signal. In this way, frequency, damping factor, real and imaginary parts of the signal are estimated. In following, the convergence analysis of both the proposed algorithms is presented. The parameters estimation of a signal corrupted with white gaussian noise is of importance in signal processing. Therefore, it is important to compare the performance of the algorithms with a criterion called Cramer-Rao lower bound (CRLB). In following, the CRLB is attained for the complex EDS signal corrupted with a complex white Gaussian noise. The performance of the proposed algorithms is compared with this bound. Various simulations show the desirable performance of the proposed algorithms at different situations. At the end, the performance of the proposed Adaline networks is compared together. Simulation results confirm the better performance of the first Adaline in estimating of the parameters of the complex biased EDS signal. Key Words: Complex exponentially damped sinusoidal signal, Frequency, Damping factor, Adaline network, Normalized LMS algorithm, Cramer-Rao lower bound (CRLB)
