Many methods have been proposed to estimate power system small signal stability, for either analysis or control, through identification of modal frequencies and their damping levels. Generally, estimation methods have been employed to assess small signal stability from collected field measurements. However, the challenge to using these methods in assessing field measurements is their ability to accurately estimate stability in the presence of noise. In this thesis a new method is developed which estimates the modal content of simulated and actual field measurements using orthogonal polynomials and the results are compared to other commonly used estimators. This new method estimates oscillatory performance by fitting an associate Hermite polynomial to time domain data and extrapolating its spectrum to identify small signal power system frequencies. Once the frequencies are identified, damping assessment is performed using a modified sliding window technique with the use of linear prediction (LP). Once the entire assessment is complete the measurements can be judged to be stable or unstable. Collectively, this new technique is known as the associate Hermite expansion (AHE) algorithm. Validation of the AHE method versus results from four other spectral estimators demonstrates the method's accuracy and modal estimation ability with and without the presence of noise. A Prony analysis, a Yule-Walker autoregressive algorithm, a second sliding window estimator and the Hilbert-Huang Transform method are used in comparative assessments in support of this thesis. Results from simulated and actual field measurements are used in the comparisons, as well as artificially generated simple signals. A search for actual field testing results performed by a utility was undertaken and a request was made to obtain the measurements of a brake insertion test. Comparison results show that the AHE method is accurate as compared to the other commonly used spectral estimators and its predictive capability exceeded the other estimators in the presence of Gaussian noise. As a result, the AHE method could be employed in areas including operations and planning analysis, post-mortem analysis, power system damping scheme design and other analysis areas.