Automatic derivation of adaptive algorithms for a large class of filter structures

Coefficient sensitivity computation is a crucial step for the derivation of adaptive gradient descent algorithms based on least mean squares or least squares criteria. Some useful tools for computing gradient vectors are summarized. These tools are based on the network sensitivity theorem and the theory of transposed networks. However, direct application of these tools gives rise to circuits which have an O(N/sup 2/) computational complexity per iteration. For a filter made up of a connection of basic cells with two access ports, it is shown how to build gradient filters using building blocks derived from the filter. The building blocks are made with basic cells and transposes of the basic cells. For simple cells, such as the lattice cells, it is possible to form the gradient filter cell following a circuit approach, i.e., the basic blocks of the gradient filter are graphically designed. Recurrence mechanisms, which are often difficult to find, are thus directly given by assemblage of the basic gradient blocks. The whole computation load results in O(N) computational complexity per iteration.<>