Analysis of adaptive FIR filters in cascade form

This paper deals with the behavior of adaptive FIR filters in cascade form. The cascade filters are investigated with simulations and analysis. The results and methods for the cascade filters are compared with the corresponding cases for the transversal filter and, especially, the well-known LMS algorithm. In the analysis, we treat a cascade filter updated with a gradient algorithm. The analysis, which uses a “slow“ adaptation assumption, gives a recursive expression for the expected value of the error in the coefficient vector. A steady-state solution for the covariance matrix of the coefficients is derived and analytical learning curves are computed. Using an assumption of accurate power measures, these results are then applied to a filter updated with a normalized gradient