Abstract
This paper proposes an adaptive digital filtering method which improves continuous-time performance. To take account of continuous-time performance, we make an assumption that the adaptive filter can exploit the continuous-time error signal, and define the integral of the square error signal as a performance index. Using lifting, the performance index can be equivalently reduced to a summation of discrete-time signals. Therefore it is shown that the recursive formula for the filtering problem with the performance index is given by the well-known RLS algorithm. Next, a more implementable case is considered where the output of the unknown system is approximated by the oversampled discrete-time signal and the summation of the squared discrete-time signals is defined as an approximate performance index. It is shown that the approximate performance index can be directly applied to the first result. Finally, some numerical examples are given to illustrate the effectiveness of the proposed method.
