RELATIONSHIPS BETWEEN ERROR SURFACES AND NETWORK ARCHITECTURES IN ADAPTIVE FILTERS.

The relationship between mean-square error (MSE) and the filter coefficients in an adaptive digital filter is often called the error-surface in (N plus 1)-dimensional parameter space. Characteristics of the error surface determine how well a gradient algorithm will perform within a given filter structure, i. e. , if the surface has steep slopes and contains local minima, a gradient algorithm will have difficulty reaching the global minimum. Most published studies deal only with error surfaces of FIRs and IIRs in direct form. The authors present an analysis of error surfaces for two other structures: 1) an FIR with an orthogonal transformation, and 2) a parallel-form IIR structure. In the FIR case it is shown how the shape of the error surface is altered by the presence of the orthogonal transform; in the IIR case it is shown how the error surface of the parallel form relates to the more familar direct form.