In this thesis, parameter estimation of a signal consisting of a number of exponentially damped sinusoidal signal (EDS) corrupted with noise is considered. It is clear that this signal with zero damping factor is a pure sinusoidal signal. Frequency estimation of a pure sinusoidal signal is frequently encountered in signal processing and control applications, for instance, in active noise control, power systems, computer hard disk drive, harmonic control, rotating mechanical systems, etc. In order to estimate the frequency of a pure sinusoidal signal many techniques have been developed such as adaptive notch filter, discrete Fourier transform (DFT) and its modifications, phase locked loop and Kalman filtering. In the case of non-zero damping factor, both damping factor and the frequency of the EDS signal should be estimated simultaneously. This kind of problem arises in several practical fields such as speech/audio analysis, linear system identification and transient analysis. In these applications, the observed signals can be modelled as noisy EDS signals. On the other hand, EDS signals are frequently encountered in the response of linear and time invariant systems. Therefore, the problem of estimating the parameters of an EDS signal in noise has been an attractive one; although its inherent nonlinearity has made it a difficult problem. Various methods have been proposed to estimate the parameters of an EDS signal. Some of well-known approaches include matrix pencil method, estimation of signal parameters via rotational invariance technique (ESPRIT), Kung’s algorithm, maximum likelihood method, linear prediction methods such as Prony’s method, Kumaresan-Tufts method. These methods are not suitable for tracking time varying parameters. Therefore researches have been focused on applying on-line estimators such as Kalman filter to track time varying frequency and damping factor. Kalman filter is considered as a recursive algorithm for optimal estimation of linear stochastic processes. This algorithm is suitable for applying in digital systems and is a reasonable choice for on-line applications because of its acceptable computational load. Extended Kalman filter represents the conversion of the Kalman filter to nonlinear processes such as frequency tracking problem. There is a long history of applying extended Kalman filter (EKF) for estimation and tracking the frequency of a pure sinusoidal signal. The frequency estimation based on EKF is particularly pertinent in view of our interest in developing an EDS signal parameters estimator. In this thesis is we drive an EKF for estimating the parameters of an EDS signal. First, a new state space model is developed for an EDS signal. Then, an EKF is designed using the linearization of the proposed state space model that provides a direct estimation of frequency and damping factor and stability analysis of the proposed algorithm is carried out. Adaptive nature of the proposed EKF enables it to track time variations of EDS signal parameters. Various simulations show the desirable performance of the proposed EKF. Furthermore, the proposed method is extended for a signal consisting of a number of exponentially damped sinusoidal signals and finally the estimated parameters are employed in an adaptive feedforward cancellation scheme to cancel the EDS type disturbances affecting a linear system. Keywords: parameter estimation, exponentially damped sinusoidal signal, EDS, extended Kalman filter, EKF, disturbance rejection