Modeling and identification of LPTV systems by wavelets

We propose a novel model for discrete linear periodic time varying (LPTV) systems using wavelets. The new model is compared with the 'raised model', which is commonly used for modeling LPTV systems. In fact, it turns out that the new model can be viewed as a generalization of the raised model. The wavelets model will be shown to be particularly suitable for adaptive identification of LPTV systems. It offers a compromise between time- and frequency-based algorithms. Time resolution is needed for modeling reasons and minimizing processing delay. Frequency resolution enables faster convergence of adaptive algorithms in general and the least mean square algorithm used here, in particular. Simulations show that for a colored input using the new model results not only in faster convergence compared to the raised model based algorithm, but also produces a lower steady-state error. This, at no significant additional cost in numerical complexity.