### AE2M31ZRE seminar Recognition of vowel sequence based on HMM - part II

Definition and construction of HMM model
Computation of emitted probabilities and passing likelihood through whole HMM model

• Definition of HMM-model transient matrix, computation of emitted probabilities in HMM states
• Determine parameters of HMM transient matrix for the supposed utterance in the following form - duration of each vowel same as separation pause is 1s. Save parameters into the structure variable hmm.a in the related HMM model. Order of the matrix A should be hmm.states+1, i.e. it is necessary to take into the account also the leaving of the last HMM state.
• Compute the matrix of all emitted log-probabilities (with suitable thresholding) for all states of given HMM model. This matrix should have the number of rows related to the number of states in HMM model and number of columns related to the number of feature vectors (short-time frames) in analyzed utterance.
• 1st checked result (1 point): Display for the utternaces P0, P1 and P2:
• Computed emitted log-probabilities for all states (use function pcolor followed by shading interp).
• Display in command prompt (or variable space) matrix of transient probabilities A.

• Computation of likelihood of passing through HMM using Viterbi algorithm
• Create function myviterbi for the computation of likelihood of passing through HMM model based on Viterbi algorithm. Input of this function should be matrix of feature vectors (cepstra) and chosen HMM model. Output should be the final likelihood of passing through HMM model.
• Determine optimum path using backtracing of passing through HMM model.
• Determine boundaries of particular vowels in utterances P0, P1 and P2.
• 2nd checked result (1 point): Display for test utterances P0, P1 and P2
• Likelihoods of passing through HMM model AEIOU for these 3 possible sequences, i.e. AEIOU, UOIEA, IUAOE.
• Display also the line representing the optimum path into the plot with emitted probabilities in all states (previous checked result).
• Waveform and spectrogram with determined phone boudaries for correct utterance P0.

• On the bsais of known boundaries, precise transient matrix A and compute on more time likelihoods of passing through HMM model with corrected transient probabilities.