tr>
 <tr><th>N</th><td>x<sub>N</sub></td></tr>
 </tbody>
 </table></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the real data array to be transformed</dd>
<dt><span class="strong">Returns:</span></dt><dd>the real transformed array, <code>y</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentExcept