Wavelets and dynamic pattern recognition

The spectral analysis in the spirit of traditional Fourier transform does not preserve the time dependence of the patterns when a signal is nonstationary. Wavelet analysis, on the other hand, has emerged as a remarkable tool for decomposition of functions. General procedures of wavelet-based regression estimators assume the time-invariant coefficients. To accommodate the stochastic and dynamic properties that are typical of many applications, we incorporate the state-space model in the wavelet estimator. The coefficients of the wavelet estimators are formulated as dynamic (random) processes so that the Kalman filtering approach can be applied. The resulting estimator is a stochastic nonlinear wavelet-based estimator.