Nonlinear system identification using a prefiltering bank with wavelet impulse responses

This paper proposes a scheme for decreasing the number of parameters identified by adaptive filters (with finite impulse response). The decrease of the computational complexity and the increase of the convergence speed are among the benefits of using the proposed identification scheme. A second order Volterra system is considered as reference system to be identified. A filter bank is used to decompose the (stationary) input signal into several components, which are then cross-multiplied and used as input sequence for an adaptive algorithm. Due to its good convergence properties, RLS is used in this paper as adaptive algorithm; current RLS implementations require a computational complexity that exponentially grows with the number of parameters. One set of functions are used for the impulse responses of the filter bank: reverse biorthogonal spline wavelet functions. The experiments are analyzed from identification accuracy, tracking capability, identified impulse response and obtained quality versus needed computational complexity points of view; RLS convergence data is provided.