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In this report, 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. A comparison of these bounds is made for the case where the input data to the Spectral Line Enhancer is composed of a single sinusoid of random phase in the presence of an additive autoregressive noise sequence. The results of extensive computer simulations of the adaptive algorithms considered are used to determine the usefulness of the theoretical bounds and to make comparisons of the performance of the four methods.