Adaptive 1-D and 2-D filtering with internally passive structures

Internally passive filters such as wave digital filters (WDF) and orthogonal filters, which have desirable properties, are developed as filter structures for adaptive filters. The equations for updating the multiplier coefficients as well as for computing the gradients are derived for these filters. The stability monitoring during the adaptation process for these filters is simple to implement. Simulation results are included to demonstrate the capability of these filters in system identification and noise cancellation. Moreover, motivated by applications of multidimensional adaptive filters in video compression and image enhancement, the proposed adaptive wave digital filters have been extended to two dimensions and applied as adaptive fan filters. Computer simulations are also conducted to show their potential applications to two-dimensional system identification and image enhancement.