Identification, parameterization and estimation of non-stationary systems using wavelet transforms

Wavelet transforms have shown some utility in problems that require simultaneous time frequency localization. Stationary systems have been analyzed and identified in both time and frequency domain. The techniques applied to stationary systems fail when applied to non-stationary systems. In this research we introduce a new method of model derivation entirely in the wavelet domain. The model is then used to estimate wavelet coefficients of the system at any arbitrary point. If we measure time series outputs of a non-stationary system and take the wavelet transform of the data; we will have a set of wavelet coefficients. These coefficients can then be treated as time series and can be parameterized as functions of time. This model can then be used to estimate and predict values.