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PART|I Signal Processing, Modelling and Related Mathematical Tools
where one also needs to keep for each max operator, the correspond-
ing argmax state. One can then recover the best sequence of states
by starting from the last state i =argmax
j
V( j, T ) and applying the
argmax operator recursively backward through the whole sequence.
2.4.5 HMMs for Speech Recognition
In the context of speech recognition, HMMs are used to estimate the
acoustic model p(
¯
x|¯w). Typically, word sequences ¯w are broken down
into sequences of smaller units, such as phonemes; a separate HMM
is then trained for each phoneme model. Afterward, phoneme HMMs
can be concatenated ...