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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Next, compute the multiresolution decomposition:</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">mra</inlineAttr></f> data structure is a matrix of (J+1) rows. Row 0 is the smooth component; the other J rows are the detailed components <region region-id="4714" left="267.75" top="1455" width="42.75" height="18" align-x="293.25" align-y="1466.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="#ffff80" tag=""><math optimize="false" disable-calc="false"><ml:sequence><ml:id xml:space="preserve" subscript="J">D</ml:id><ml:id xml:space="preserve" font="1">...</ml:id><ml:id xml:space="preserve" subscript="1">D</ml:id></ml:sequence></math><rendering item-idref="37" /></region>.</p>
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          <c val="#000">The fine scale features (the high frequency oscillations at the beginning of the signal) are captured mainly by the fine scale detail components D</c>
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          <c val="#000"> and D</c>
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          <c val="#000">correspond to the lower frequency oscillations. </c>
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        <phrase>high-frequency oscillation</phrase>
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        <p style="Heading 1" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The Multiresolution Approximation</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">By zooming in and out using the multiresolution approximations <c val="#000">S</c><c val="#000"><sub>0</sub></c><c val="#000">(t)</c>, <c val="#000">S</c><c val="#000"><sub>1</sub></c><c val="#000">(t)</c>, <c val="#000">S</c><sub><c val="#000">2</c></sub><c val="#000">(t)</c>, etc., you can focus on different features of the signal. The coarse scale approximation <c val="#000">S</c><c val="#000"><sub>6</sub></c><c val="#000">(t)</c> gives a "faraway view" of the signal: you can see the overall shape, but dome detail is lost. The fine scale approximations give a "close-in view" for the signal, revealing more detail but also more noise.</p>
      </text>
      <indexes>
        <phrase>signal, close-in view</phrase>
        <phrase>signal, faraway view</phrase>
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