●Signal Models ●Markov Chains ●Hidden Markov Models ●Fundamentals for HMM Design

●Are used to characterize real world signals. ●Provide a basis for a theoretical description of a signal processing system. ●Tell about the signal source without having the source available. ●Are used to realize practical systems efficiently. 2 Types of Signal Models: ●Deterministic Models:- Specific properties of the signal are known. eg. The signal is a sine wave- Determining values for parameters of the signal, such as frequency, amplitude, etc is required. ●Statistical Models:- eg. Gaussian processes, Markov processes, Hidden Markov processes- Characterizing the statistical properties of the signal is required.- Assumption: * Signal can be characterized as a parametric random process. * Parameters of the random process can be determined in a precise and well defined manner. Discrete Markov Processes [1] ● The system is described by N distinct states: