Adaptive linear estimation algorithms applied to spectral line enhancement

In this dissertation, two adaptive algorithms based on fixed point iteration methods and using direct estimates of the required statistics are proposed. These algorithms are slightly more complex than the LMS Gradient Algorithm but have the advantage that the amount of computational effort required during each sample period can be varied. Thus, tradeoffs can be made between the number of operations required per sample and the rate of convergence of the algorithm. The performance characteristics of the LMS Gradient Algorithm, two Adaptive Fixed-Point Iteration Algorithms and of a non-iterative method based on Levinson's Algorithm are considered for the case where an adaptive algorithm is used to determine the unit sample response for a system which attempts to discriminate between the signal and noise processes on the basis of bandwidth. Such a system is often referred to as a Spectral Line Enhancer. Theoretical bounds on the mean square error as a function of the time index n are derived for each of the three iterative methods.