ABSTRACT
This chapter reviews the direct form gradient descent algorithm, which is the workhorse of adaptive infinite impulse response (IIR) filtering. It presents an introduction to a convergence analysis approach based on an associated differential equation. The chapter shows how the gradient computations can be reduced to order M complexity by a clever rearrangement of the computations due to Rodriguez-Fonollosa and Masgrau. It examines the rotation parameter gradients under the constraint that the tap parameters are optimized. The chapter pursues further simplifications to the partial gradient algorithm. It presents specific reformulations of the update algorithm for the rotation angles of the lattice filter, to obviate the need to evaluate trigonometric functions. The basic idea is to associate to a discrete-time parameter adaptation algorithm an ordinary differential equation, in such a way that the convergence properties of the former are strongly or weakly tied to the stability behavior of the latter.
