Time-varying adaptive filters for evoked potential estimation

Adaptive implementation of an optimal time-varying filter (TVF) for evoked potential (EP) estimation is addressed in this paper. A data-adaptive scheme is used, which converges asymptotically to the optimal TVF solution. Two basic adaptive TVF's (ATVF's) are first introduced, namely least mean square (LMS) ATVF and recursive least-squares (RLS) ATVF. The latter converges much faster than the former. Since the basic ATVF's usually require a relatively large set of response trials to get a meaningful solution, a reduced-order ATVF is further presented and the corresponding LMS and RLS (including a fast RLS) adaptive algorithms are developed. To save memory, a truncated Fourier expansion is suggested to express approximately the time-sequenced weight-vectors of the ATVF's, resulting in a simplified reduced-order ATVF. Finally, extensive simulations are provided to confirm the superior performance of the ATVF's. The present ATVF's can be used as prefilters for latency-corrected average (LCA) processing to obtain more informative estimates of EP signals.