A second order hyperstable adaptive filter with no post-error filtering

A second-order hyperstable adaptive recursive filter is presented, that does not require the usual post-error filtering that is needed in other hyperstable adaptive schemes to guarantee convergence. The filter is developed for the particular application of frequency estimation of an input sinusoid, rather than as a general infinite impulse response (IIR) adaptive filter. As the adaptive algorithm can be made to converge arbitrarily fast by increasing the μ value, while still retaining stability, it may be used in situations where the input frequency changes have to be tracked very fast, as for instance in frequency hopped spread spectrum M-ary frequency (MFSK) communication systems etc