Modeling and identification of time-varying systems - A wavelet approach

The present work proposes a methodology for modeling and identification of boundedinput bounded-output (BIBO) time-varying (TV) system impulse responses based on a wavelet approach. This approach permits representation of a time-varying system impulse response in the auxiliary domains, commonly referred to as the transform domains. The latter includes the well-known discrete wavelet transform (DWT) as well as the pure frequency domains. This work is organized as follows. First, a norm is defined for BIBO time-varying system impulse responses, and the set of all BIBO systems is shown to be a Banach space with respect to the defined norm. Next, the problem of modeling the time domain system impulse responses in the transform domain is investigated. Three different but related transformations are discussed. Thirdly, the present work provides discussion on representing modeling uncertainties in both the time and the transform domain. The relations between two domains are discussed. System identification in the transform domain is also investigated in the present paper. Finally, based on modeling of system impulse responses, the system linking is proposed in pure transform domain. An example is provided to show the use of modeling uncertainty measures and transform domain system identification.Ope