Time map domains

                                                     

In the autosegmental representation of the syllable /dOk/ above, we indicated that a temporal interpretation is possible. The sequencing of information along the tiers is defined with respect to a temporal relation of precedence and the association between information on separate tiers is defined with respect to the temporal relation of overlap. Thus it is not required that overlapping autosegments have the same inherent duration but can vary with respect to their individual properties. Although this interpretation incorporates a temporal dimension into the representation by introducing the notion of an event defined with respect to property and time interval, this does not go far enough for speech applications where actual temporal annotations are required. Let us assume three temporal domains which refer to different perspectives on spoken language utterances: T$_{\rm cat}$, the category or hierarchical time domain,  T$_{\rm rel}$the relative time domain and T$_{\rm abs}$the absolute time domain.

In the relative time domain, we are interested in the temporal relations which exist between features in an autosegmental representation. In the absolute time domain, on the other hand we are interested in token utterances with actual temporal annotations. What is required in speech recognition, for example, is a mapping from the absolute time annotations to a relative time domain in which the actual time is no longer required. Likewise, speech synthesis requires a mapping from the relative time domain to the absolute time domain since here also temporal annotations or at least average durations are required.

In the rest of this section we will concentrate on the the relative time domain. We will return to the absolute time domain in the section on linguistic word recognition. In order to incorporate temporal relations into our description of syllables we must define the symbols for precedence (<) and overlap (). We can incorporate this information into our representation by invoking an FST in our general Syllable definition: 

Syllable:
    ...
    <rel-time> == Relations:<<>>.
The first two equations of the Relations transducer are just a version of the IDEM transducer discussed in the section on finite state transducers, above (but where variable $G ranges over features and square brackets). The next three equations simply delete any empty feature bundles ([ ]). And the final pair of equations introduce the temporal relations into the representation (where variables $F1 and $F2 range over features). 
Relations:
    <>        == Null
    <$G>      == $G <>
    <[ ]>     == <>
    <[ [ ]>   == <[>
    <] [ ]>   == <]>
    <] [>     == ] '<' <[>
    <$F1 $F2> == $F1 o <$F2>.

We can now infer the following feature information for the example syllable /dOk/: 

S_dOk:
<rel-time structure featural> =
       [ [ [voiced] o [plosive] o [alveolar] ] ] 
                        <
       [ [ [voiced] o [vowellike] o [back] o 
           [mid] o [round]  o [lax] ] ]
                        <
       [ [ [voiceless] o [plosive] o [velar] ] ]

Exercise 6051

Show the (transduced) feature information for S_tee, S_E6 and the ten segment syllable node that you constructed for an earlier exercise.

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