Many techniques have been developed to analyze time series. Spectral analysis and cycle regression analysis represent two such techniques. This study combines these two powerful tools to produce two new algorithms; the spectral algorithm and the one-pass algorithm. This research encompasses four objectives. The first objective is to link spectral analysis with cycle regression analysis to determine an initial estimate of the sinusoidal period. The second objective is to determine the best spectral window and truncation point combination to use with cycle regression for the initial estimate of the sinusoidal period. The third is to determine whether the new spectral algorithm performs better than the old T-value algorithm in estimating sinusoidal parameters. The fourth objective is to determine whether the one-pass algorithm can be used to estimate all significant harmonics simultaneously.