Because speech recognition has been the most
common application of HMMs, we will discuss
here some of the issues it involves, although
this discussion is relevant to many other
applications. The basic speech recognition
problem can be stated as follows: given
a sequence of acoustic descriptors (obtained
by pre-processing the speech signal, e.g.,
spectral information represented by a vector
of between approximately 10 and 40 numbers,
obtained at a rate of around 10 millisecond
per time step), find the sequence of words
intended by the speaker who pronounced those
words. Training data for solving this task consists
of a large set of labeled sequences, i.e., pairs
,
where
is a word sequence and
is an acoustic
sequence,
is an element from a finite set of words,
and
is a real vector.
Figure 5: Example of application of HMMs to
isolated word recognition. There is a single
HMM for each word in the vocabulary (represented by
an oval in the figure), here left-to-right with
skips. The recognizer picks the word w
with the highest probability
,
given the acoustic sequence
.