Convergence analysis and fast algorithms of Volterra adaptive filters

In this paper, tight upper and lower bounds arc obtained for all of the eigenvalues of co variance matrices in quadratic Volterra adaptive filters with Gaussian input signal. It is shown that the error surface of quadratic Volterra ADF is always extremely steep in one particular direction but relatively flat in the rest directions. Based on these analysis, fast converging adaptive algorithms for both white and colored input signals arc presented.