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<div><h1 id="a0000000095">1.19 fft</h1>
<p><a name="a0000001023" id="a0000001023"></a> </p><pre>
fft {&lt;range&gt;} &lt;function&gt;"()"
    of ( '&lt;filename&gt;' | &lt;function&gt;"()" )
    [using &lt;expression&gt; {:&lt;expression&gt;} ]

ifft {&lt;range&gt;} &lt;function&gt;"()"
    of ( '&lt;filename&gt;' | &lt;function&gt;"()" )
    [using &lt;expression&gt; {:&lt;expression&gt;} ]
</pre><p>The <tt class="tt">fft</tt> command<a name="a0000001024" id="a0000001024"></a> calculates Fourier transforms of datafiles or functions. Transforms can be performed on datasets with arbitrary numbers of dimensions. To transform an algebraic expression with <img src="images/img-0014.png" alt="$n$" style="vertical-align:0px; 
                                     width:11px; 
                                     height:8px" class="math gen" /> degrees of freedom, it must be wrapped in a function of the form <img src="images/img-0629.png" alt="$f(i_2,i_2,\ldots ,i_ n)$" style="vertical-align:-4px; 
                                     width:115px; 
                                     height:18px" class="math gen" />. To transform an <img src="images/img-0014.png" alt="$n$" style="vertical-align:0px; 
                                     width:11px; 
                                     height:8px" class="math gen" />-dimensional dataset stored in a datafile, the samples must be arranged on a regular linearly-spaced grid and stored in row-major order. For each dimension of the transform, a range specification must be provided to the <tt class="tt">fft</tt> command in the form </p><pre>
[ &lt;minimum&gt; : &lt;maximum&gt; : &lt;step&gt; ]
</pre><p>When data from a datafile is being transformed, the specified range(s) must precisely match those of the samples read from the file; the first <img src="images/img-0014.png" alt="$n$" style="vertical-align:0px; 
                                     width:11px; 
                                     height:8px" class="math gen" /> columns of data should contain the values of the <img src="images/img-0014.png" alt="$n$" style="vertical-align:0px; 
                                     width:11px; 
                                     height:8px" class="math gen" /> real-space coordinates, and the <img src="images/img-0165.png" alt="$n+1$" style="vertical-align:-1px; 
                                     width:41px; 
                                     height:13px" class="math gen" />th column should contain the data to be transformed. After the range(s), a function name should be provided for the output transform: a function of <img src="images/img-0014.png" alt="$n$" style="vertical-align:0px; 
                                     width:11px; 
                                     height:8px" class="math gen" /> arguments with this name will be generated to represent the transformed data. Note that this function is in general complex – i.e. it has a non-zero imaginary component. Complex numerics can be enabled using the <tt class="tt">set numerics complex</tt> command and the <tt class="tt">fft</tt> command is of little use without doing so. The <tt class="tt">using</tt>, <tt class="tt">index</tt>, <tt class="tt">every</tt> and <tt class="tt">select</tt> modifiers can be used to specify how data will be sampled from the input function or datafile in an analogous manner to how they are used in the <tt class="tt">plot</tt> command. </p><p>The <tt class="tt">ifft</tt> command calculates inverse Fourier transforms; it has the same syntax as the <tt class="tt">fft</tt> command. </p></div>





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