Representation and identification of systems in the wavelet transform domain
Yekutiel Avargel, Israel Cohen · 2007
In this paper, we introduce an explicit representation of linear time-invariant system in the discrete-time wavelet transform (DTWT) domain. It is shown that crossband filters between subbands are required for perfect representation of the system. These filters depend on the DTWT parameters and on the system impulse response, and are shown to be time-varying. An approximate representation based on band-to-band filters without crossband filters is employed for system identification in the wavelet domain. We show that for longer and stronger input signals, longer band-to-band filters may be estimated. Experimental results validate the theoretical analysis and demonstrate the proposed system identification approach.