System identification based on wavelet packets decomposition

This paper is concerned with a new system identification approach based on the wavelet packets (WP) decomposition. The impulse response in the WP transform domain is estimated by using the least squares (LS) method by use of the transformed input/output data. Then the estimate of the original impulse response can be reconstructed from the estimate in the transform domain by using the property of the inverse WP transform. The mean square error (MSE) is evaluated and investigated, then it is clarified that the MSE can be minimized by an optimal choice of the resolution level and the packets. Therefore, it will be very effective in ill-conditioned system identification using a band-limited input signal.