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              <c val="#008080">Appendix E: Test Signals and Other Useful Functions</c>
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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">Root mean square estimate of error which can accept a matrix, a row vector, or a column vector. </p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">These cost functions can be used with the function <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">best_basis</inlineAttr></b></f>:</p>
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        <phrase>best_basis function</phrase>
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        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">nrm is equal to the square root of the sum</p>
        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">of the squares of the data values.</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 threshold constant can be changed to anything.</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">The following two functions return matrices filled with zeroes. <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false"><c val="#008080">zeroMsq</c></inlineAttr></b></f> returns a square matrix, <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false"><c val="#008080">zeroM</c></inlineAttr></b></f> a rectangular one.</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 following functions work together to find a basis based on a threshold. <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false"><c val="#008080">Flatten</c></inlineAttr></b></f> converts a matrix to a vector for sorting. The function <b><c val="#008080">findThresh</c></b> returns a threshold which is greater than Percent of the coefficients. For a matrix, it calls <b><c val="#008080">Flatten</c></b> to convert the matrix to a vector for sorting.</p>
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        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">This function implements the up-sample by 2 operation. The up-sample by 2 operation causes image sizes to increase. </p>
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