A UNIFYING TREATMENT OF GENERAL GRADIENT ADAPTIVE DIGITAL-FILTER AND CONVERGENCE ANALYSIS WITH ARBITRARY INPUTS

The unifying treatment of a general gradient adaptive algorithm studie d here is based on the principles of minimum mean square method and in strumental variable method by formulating the general oblique projecti on algorithm, including finite impulse response (FIR) and serial-paral lel infinite impulse response (IIR)-type configurations. The oblique p rojection algorithm of low-order past-value data space is derived in w hich the dimension of past-value data space can be easily adjusted, in cluding the least mean square (LMS) method, learning-identification me thod and gradient instrumental variable method (GIVE). Next, the new a nalysis model which describes the convergence process of general gradi ent algorithm is shown and the convergence conditions are indicated fo r the first and second moments with arbitrary inputs. It is found that this condition is more severe as compared with the white input. Moreo ver, the process of convergence of these conditions is studied by simu lation.