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Question: What is HMM? What is hidden it? Draw a state diagram for HMM as general case and show how you can write a transition matrix
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Subject: Speech Processing

Topic: Speech Processing Applications

Difficulty: High

sp(38) • 375 views
 modified 3 months ago by written 4 months ago by awari.swati831 • 160
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(i) A Hidden Markov Model (HMM) is a statistical Markov model where a system to be modeled is assumed as a Markov Process with unobserved or hidden states.

(ii) A strategy which make use of stochastic model of speech production is known as Hidden Markov Model (HMM). It is found to offer performance comparable to time warping at a function of the computational cost.

(iv) This model has been explored by many researchers. In the case of HMM, a model is capable of being in only in a finite number of difference states.

(v) HMM for speech recognition will have each state capable of generating finite number of possible outputs.

(vi) In generating a word, the system passes from one state to another. Each state emits an output until the entire word is out. Such a model is illustrated in the figure below. It is called the state transition diagram.

(vii) In the case of regular Markov Model, the state is directly visible to the observer and therefore the state transition probabilities are consider as only parameter.

The transition matrix for figure is as follows:

$$A = \begin{bmatrix} 0.3 & 0.5 & 0.1 & 0 & 0.1 \\ 0.2 & 0.4 & 0.4 & 0 & 0 \\ 0 & 0.1 & 0.3 & 0.5 & 0.1 \\ 0 & 0.1 & 0.1 & 0.5 & 0.3 \\ 0.2 & 0 & 0 & 0.2 & 0.6 \end{bmatrix}$$