One can model the phonocardiogram signal as a four
state HMM. The first state corresponds to the S1 sound,
the second state corresponds to the silence during the
systolic period, the third state corresponds to the S2
sound, and the fourth state corresponds to the silence
during the diastolic period (see Figure 1). This model
ignores the possibility of the S3 and S4 heart sounds,
because these heart sounds are not germane to the task of
recognizing respiration rates from heart sound data.
Additionally, these sounds are difficult to hear and
record; therefore, they are most likely not noticeable in
our heart sound data.
This four state HMM is useful for modeling the
sequence of symbols (or labels) of the phonocardiogram;
however, it is too simple to accurately model the
transitions between sound and silence. One solution is to
embed another HMM inside of each of the heart sound
symbol states. The embedded HMM models the signal as
it traverses a specific labeled region of the signal. Using
this combined approach, we can model both the highlevel
state sequence of our signal (S1-sil-S2-sil) and the
continuous transitions of the signal. This type of model is
similar to how a speech processing system has a highlevel
probabilistic grammar to model the transition of
words or phonemes, and an embedded HMM for each
phoneme [8].
All of the experiments utilized an eight state HMM for
the S1 sounds, a six state HMM for the S2 sound, and a
three state HMM for each silence period. The number of
states where calculated by taking the average duration of
each heart sound, and dividing by the frame duration. For
example, the S1 sound has an average duration of 160
milliseconds and the frame step size is 20 milliseconds;
therefore, it can be represented by eight states (160 ms /
20 ms = 8).
In addition, the experiments utilized a four state
grammar that represented the state model given in Figure
1. The probabilities for this model were learned using a
discrete HMM where the label files were used to train the
model. The resultant HMM represents the symbol
transitions of the phonocardiogram. We manually
translated the discrete HMM into a grammar for use with
the HTK toolset [8].
One can model the phonocardiogram signal as a fourstate HMM. The first state corresponds to the S1 sound,the second state corresponds to the silence during thesystolic period, the third state corresponds to the S2sound, and the fourth state corresponds to the silenceduring the diastolic period (see Figure 1). This modelignores the possibility of the S3 and S4 heart sounds,because these heart sounds are not germane to the task ofrecognizing respiration rates from heart sound data.Additionally, these sounds are difficult to hear andrecord; therefore, they are most likely not noticeable inour heart sound data.This four state HMM is useful for modeling thesequence of symbols (or labels) of the phonocardiogram;however, it is too simple to accurately model thetransitions between sound and silence. One solution is toembed another HMM inside of each of the heart soundsymbol states. The embedded HMM models the signal asit traverses a specific labeled region of the signal. Usingthis combined approach, we can model both the highlevelstate sequence of our signal (S1-sil-S2-sil) and thecontinuous transitions of the signal. This type of model issimilar to how a speech processing system has a highlevelprobabilistic grammar to model the transition ofwords or phonemes, and an embedded HMM for eachphoneme [8].All of the experiments utilized an eight state HMM forthe S1 sounds, a six state HMM for the S2 sound, and athree state HMM for each silence period. The number ofstates where calculated by taking the average duration ofeach heart sound, and dividing by the frame duration. Forexample, the S1 sound has an average duration of 160milliseconds and the frame step size is 20 milliseconds;therefore, it can be represented by eight states (160 ms /20 ms = 8).In addition, the experiments utilized a four stategrammar that represented the state model given in Figure1. The probabilities for this model were learned using adiscrete HMM where the label files were used to train themodel. The resultant HMM represents the symboltransitions of the phonocardiogram. We manuallytranslated the discrete HMM into a grammar for use withthe HTK toolset [8].
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