Frequency estimation of sinusoidal signals is a fundamental question in systems theory and signal processing that has many practical applications in different areas of electrical engineering such as active noise and vibration control in helicopters, disk drives and magnetic bearings. control and system identification, biomedical engineering, control and power system protection, communication and radar. There exist several algoritms to estimate online the frequency of a sinusoid. Adaptive notch filtering is a well known method for frequency estimation with properties of accuracy and capability of tracking. The adaptive notch filter (ANF) is a second-order notch filter equipped with a nonlinear differential equeation to update the frequency. The structure is capable of changing the notch frequency accordingly by tracking the frequency varations of the sinusoidal signal. The realization of adaptive notch filter (ANF) in discrete-time domain is of practical importance. In this thesis, discretization of an ANF is done in two methods, i) state-space discretization method, ii) pole zero matched method (Tustin method with frequency pre warping).In the first method, the state-space realization of the notch filter is desceritized, while in the second method the notch filter transfer function is desceritized using the pole-zero matched. The frequency update law is desceritized by forward method in both proposed discrete-time ANF. Existance of a periodic orbit preserves accurace frequency estimation. Detailed stability analysis of both proposed discrete-time ANFs is carried out on the basis of local averaging theory under the assumption of slow adaptation. Also, a method for controlling the bandwidth of second discrete-time ANF is proposed in this thesis. This method is based on the gradient descent algorithm and provides the desirable bandwidth for ANF. Simulation results verify the validity of the presented methods and confirm their desirable transient and steady-state performances as well as their desirable noise characteristics. Also, the simulations show the robust performance of proposed ANFs at low sampling frequency. Keywords: frequency estimation, sinusoidal signal, adaptive notch filter, discretization, stability analysis, sampling frequency, bandwidth adjustment.