Improving the Estimation Accuracy of Signals with Low Signal-to-Noise Ratio Using Optimal Combining Methods

An integral component of analyzing a signal lies in our ability to successfully remove noise and interference from the signal under consideration. In most applications, weak signal or a large amount of noise resulting in a low signal-to-noise ratio (SNR) makes this process challenging. In this thesis, we investigate several methods to increase the SNR in processes that involve multiple measurements, with measurements being completed simultaneously or in multiple trials over time. These methods are applicable to a variety of disciplines, ranging from astrophysics, for processing signals from radio telescope arrays, to biomedical applications, including interpreting electroencephalogram (EEG) and event-related potential (ERP) data. The primary method pursued in this thesis is a minimum variance linear estimation technique that finds optimum coefficients to minimize the estimation error. A second method is used to distinguish between frequency components of the signal and noise to remove the noisy components through use of a soft threshold. Both methods make use of a common assumption used in ERP signal processing techniques; the recorded response not associated with the stimulus has zero mean, and thus will sum to zero when multiple trials are averaged. This project provides a comprehensive analysis of ERP data from four newborns utilizing the aforementioned methods. Simulation results demonstrate the noise reduction capabilities for both methods.