Computationally efficient algorithm for adaptive quadratic Volterra filters

The structure of the input autocorrelation 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 autocorrelation matrix of quadratic filter 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 correlation matrix that results from this formulation.