Parametric Estimate Of Wavelet Transformation On Hidden Markov Processes

Hidden Markov Models(HMM) have been widely used in pattern recognition and stochastic signal processing in recent years, and the best examples are speech recognition and character recognition. As we know, whether the input signals are normal has become one of the most important factors for performance of a pattern recognition system. Therefore, in order to improve robustness of a recognition system, we need to construct a hidden Markov model which can withstand noise and adapt itself to the input signals. Because wavelet transformation has strong capability of withstanding noise, we have easily considered making wavelet transformation for the input signals, and recognizing them in hidden Markov models.In this thesis, we first introduce some basic elements in hidden Markov models, and consider three basic problems we shall encounter when hidden Markov models are used in reality. Also, we give the corresponding resolutions. Then we introduce some special structures in hidden Markov models.Second, we consider wavelet transformation and the related knowledge. After simply introduce the development of wavelet transformation, we mainly consider the important theory in wavelet transformation-multi-resolution analysis theory, and the corresponding algorithm-Mallat algorithm.Finally, a new method to adapt the parameters of hidden Markov models is proposed when the input signals are transformed by wavelet. By our method, we are able to be free from the requirement of retraining the whole recognition parameters when the input signals are changed and makes it sufficient to adapt the parameters to the given impulse response of wavelet filter.