Various spectral estimation methods are investigated for the purpose of tracking the frequencies of the given time series data including sampled speech signals. Analysis and numerical results yield that discrete Fourier transformation (DFT), widely-used autoregressive modeling (AR) and unmodified composite sinusoidal modeling (CSM) fail to track rapidly changing frequencies. A chirp Z transform (CZT) is used to overcome this problem. In addition, the AR and CSM are modified to improve tracking capabilities of the rapidly changing frequency. Development of the modified methods is described in the thesis. A fast algorithm to solve Hankel system of equations arisen from CSM is developed based on Kumar's equation and detailed analysis is also presented in the thesis. Numerical simulations of sinusoids with varying frequencies and applications to track the formant frequencies of speech signals are treated.