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In a typical speech recognition system, the reference and test
features are not aligned in time
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Time alignment means the process by which temporal regions
of test utterances are matched with appropriate regions
of reference utterances
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The test and reference are arranged along the i-j axis as
shown. The objective is to match the test and reference
features so that they are properly aligned
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Let d(ik,jk) be the cost of matching
the t(ik) with r(jk)
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Then the global cost of th entire match is given by