# Spectral estimators for narrowband signals embedded in correlated and uncorrelated noise

## Description

This dissertation introduces filter structures and adaptive algorithms for spectral estimation of narrow-band signals in uncorrelated and correlated noise. A new expression of the misadjustment in the LMS algorithm is derived. Earlier expressions are shown to be approximations of this new expression. Also, new upper and lower bounds of the misadjustment are found. This new expression of the misadjustment is used to analyze the performance of the FIR ALE, when the LMS algorithm is used to estimate its weights. It is shown that the performance of the FIR ALE is a function of the frequency of the sinusoid that is present in the data. Another filter structure, the IIR ALE is used to estimate the frequency of a real-time physiological signal. The adaptive parameter in the IIR ALE is found to converge to the frequency value in as low as 20 iterations. The IIR ALE is implemented in a lattice filter form. It is interpreted as an ARMA whitening filter and translated to the lattice structure. This results in computational savings per iteration and faster convergence by almost a factor of two. A new filter structure for spectral estimation is introduced. This method adaptively estimates the eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix of the input data. This structure also works effectively when the sinusoidal signal is embedded in correlated noise