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<meta itemprop="keywords" content="Analysis toolpack,Fourier analysis">
<meta itemprop="keywords" content="Fourier analysis,Analysis toolpack">
<meta itemprop="keywords" content="Data statistics,Fourier analysis">
<a name="fourieranalysis"></a>
<h1 id="hd_id431561808831965" dir="auto">
<a name="fourieranalysysh1"></a>Fourier Analysis</h1>
<p id="par_id1001240" class="paragraph" dir="auto"><span class="avis">Produces the Fourier analysis of a data set by computing the Discrete Fourier Transform (DFT) of an input array of complex numbers using a couple of Fast Fourier Transform (FFT) algorithms.</span></p>
<a name="howtoget"></a><div class="howtoget">
<div><p class="howtogetheader" dir="auto"><a name="wie"></a>To access this command...</p></div>
<div class="howtogetbody">
<p id="par_id1000040" class="paragraph" dir="auto"><a name="sam01"></a>Choose <span class="menuitem">Data - Statistics - Fourier Analysis</span></p>
</div>
</div>
<br>
<div class="note">
<div class="noteicon" dir="auto"><img src="media/icon-themes/res/helpimg/note.svg" alt="note" style="width:40px;height:40px;"></div>
<div class="notetext"><p id="par_id1001270" dir="auto">For more information on Fourier analysis, refer to the <a target="_blank" href="https://en.wikipedia.org/wiki/Fourier_analysis">corresponding Wikipedia article</a>.</p></div>
</div>
<br>
<div class="embedded">
<a name="data"></a>
<h3 id="hd_id1000010" dir="auto">Data</h3>
<p id="par_id1000010" class="paragraph" dir="auto"><span class="emph">Input Range</span>: The reference of the range of the data to analyze.</p>
<p id="par_id1000020" class="paragraph" dir="auto"><span class="emph">Results to</span>: The reference of the top left cell of the range where the results will be displayed.</p>
</div>
<p id="par_id301561811172762" class="paragraph" dir="auto"><span class="emph">Input range has label</span>: Mark when the first row or column of the input array is actually a label and not part of the data analysis.</p>
<p id="par_id741556228390897" class="paragraph" dir="auto">Input Range is a 2 x N or N x 2 range representing an array of complex number to be transformed, where N is the length of the array. The array represents the real and imaginary parts of the data.</p>
<div class="embedded">
<a name="grouped"></a>
<h4 id="hd_id1000020" dir="auto">Grouped By</h4>
<p id="par_id1000030" class="paragraph" dir="auto">Select whether the input data has <span class="emph">columns</span> or <span class="emph">rows</span> layout.</p>
</div>
<h3 id="hd_id211561811324208" dir="auto">Options:</h3>
<p id="par_id631556228516997" class="paragraph" dir="auto"><span class="emph">Inverse</span>: When checked, calculates the inverse Discrete Fourier Transform.</p>
<p id="par_id811561732287508" class="paragraph" dir="auto"><span class="emph">Polar</span>: When checked, the results are in polar coordinates (magnitude, phase).</p>
<p id="par_id661561732521977" class="paragraph" dir="auto"><span class="emph">Minimum magnitude for polar form output (in dB)</span>: used only when output is in polar form. All frequency components with magnitude less than this value in decibels will be suppressed with a zero magnitude-phase entry. This is very useful when looking at the magnitude-phase spectrum of a signal because there is always some very tiny amount of rounding error when doing FFT algorithms and results in incorrect non-zero phase for non-existent frequencies. By providing a suitable value to this parameter, these non-existent frequency components can be suppressed.</p>
<div class="embedded">
<a name="func_fourier"></a>
<p id="par_id591561765191143" class="paragraph" dir="auto"></p>
</div>
<div class="embedded">
<a name="func_head_example"></a>
<h3 id="hd_id980889808898088" dir="auto">Examples</h3>
</div>
<p id="par_id731561827207828" class="paragraph" dir="auto">The source data for this example is the same of the <a target="_top" href="en-US/text/scalc/01/func_fourier.html">FOURIER function page</a>.</p>
<table border="1" class="" cellpadding="0" cellspacing="0">
<tr>
<th rowspan="" colspan="2" class="tableheadcell" dir="auto">
<p id="par_id290620191257279817" class="tableheadintable" dir="auto">Fourier Transform</p>
</th>
<td rowspan="" colspan="" dir="auto">
</td>
<th rowspan="" colspan="2" class="tableheadcell" dir="auto">
<p id="par_id29062019125727379" class="tableheadintable" dir="auto">Fourier Transform</p>
</th>
</tr>
<tr>
<td rowspan="" colspan="2" dir="auto">
<p id="par_id290620191257276510" class="tablecontentintable" dir="auto"><span class="emph">Input data range : $B$6:$C$40</span></p>
</td>
<td rowspan="" colspan="" dir="auto">
</td>
<td rowspan="" colspan="2" dir="auto">
<p id="par_id290620191257273433" class="tablecontentintable" dir="auto"><span class="emph">Input data range : $B$6:$C$40</span></p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id290620191257273688" class="tablecontentintable" dir="auto"><span class="emph">Real</span></p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id290620191257276202" class="tablecontentintable" dir="auto"><span class="emph">Imaginary</span></p>
</td>
<td rowspan="" colspan="" dir="auto">
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id481561825547527" class="tablecontentintable" dir="auto"><span class="emph">Magnitude</span></p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id751561825556834" class="tablecontentintable" dir="auto"><span class="emph">Phase</span></p>
</td>
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<tr>
<td rowspan="" colspan="" dir="auto">
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<p id="par_id901561825568423" class="tablecontentintable" dir="auto">2.26245884628906E-16</p>
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