Algorithms for improved performance in adaptive polynomial filters with Gaussian input signals

The structure of the input covariance matrix in Volterra second order adaptive filters for general colored Gaussian input processes is analyzed to determine how to best formulate a computationally efficient fast adaptive algorithm. It is shown that when the input signal samples are ordered properly within the input data vector, the covariance matrix inherits a block diagonal structure, with some of the sub-blocks also having diagonal structure. Some new results in developing and evaluating computationally efficient quasi-Newton adaptive algorithms are presented that take advantage of the sparsity and unique structure of the covariance matrix that results from this formulation.