A second-order hyperstable adaptive filter for frequency estimation

A second-order adaptive filter structure that can be used for frequency estimation and enhancement of an input sinusoid is proposed. Unlike other gradient-based adaptive line enhancement schemes, this filter has the advantage that it can be made to converge arbitrarily fast by increasing the step size of the update, while still retaining stability. This is possible because the adaptation strategy has its roots in hyperstability theory. A limitation of the scheme is that it gives a biased estimate in the presence of noise; however, some techniques that bring the bias down to a low level are described