Impulse response identification by use of 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 via the least squares method using transformed input/output data. Then the estimate of the original impulse response can be reconstructed from that in the transform domain by using the inverse WP transform. The MSE of the estimate is investigated, and it is clarified that the MSE can be minimized by an optimal choice of the threshold level, the resolution level and the packets selection. Therefore, the data adaptive choice is effective in ill-conditioned system identification using a band-limited input signal.