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
Occupacy likelihood of particular states of HMM (Backward Viterbi algorithm)
Tasks to do:
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.
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.
Result: Display for
the utternaces P1, P2
and P3 :
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.
Checked result (3 points): Display for
test utterances containing sequences of vowels:
Likelihoods of passing through HMM model AEIOU for these 3
possible sequences, i.e. AEIOU, UOIEA, IUAOE.
Determine optimum path using backtracing of passing through HMM model.
Determine boundaries of particular vowels in utterances P1, P2
Optional result (BONUS 1 point): Display for
test utterances P1, P2
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 P1.
On the basis of known boundaries, precise transient matrix A and
compute on more time likelihoods of passing through HMM model with
corrected transient probabilities.
Occupacy likelihood of particular states of HMM
In prepared function myviterbi save also the matrix of all
forward probabilities alpha related to each state and time
during the passing through HMM model.
Create also the
functions mybackviterbi (analogous to myviterbi) which
realizes backward computation of passing likelihood through HMM
(i.e. from the last state to the first one using
probabilities beta). Take as an input of this function again
the matrix of feature vectors nad given HMM model. The output should
be global probability of passing through the model same as the
matrix of all backward probabilities beta for each state and
Optional result (BONUS 1 point):
display for utterances P1, P2
computed forward and backward probabilities of passing through
HMM model for the utternace AEIOU,
occupacy likelihood for all states and all times (attention, it
is necessary to use same colorscaling when occupaccy likelihood is
presented for different utterances P1, P2 and P3.
Both BONUS results should be delivered within the previous solution of basic Viterbi decoding and the same above mentioned WEB interface.
Try also the computation of probabilities using standard
forward or backward procedure respectively.