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<HTML>
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<TITLE>Fourier coefficients</TITLE>
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<BODY bgcolor="#FFFFFF" fgcolor="#000000">
<P><font size="+3" color="green"><B>Fourier coefficients</B></font></P>
<p>
If the <CODE>COS&SIN</CODE> keyword is used,
then the <CODE>FFT</CODE> function returns the
actual Fourier coefficients.</p>
<p>
Let the cosine coefficients be called <img src="fftI01.png"> 's and let the
sine coefficients be called <img align="bottom" src="fftI02.png"> 's.
<img align="top" src="fftI03.png"> is
the mean value of the input data. As shown in the example below, these coefficients can be
used for smoothing and interpolation. Suppose <img align="bottom" src="fftI04.png"> is the
interpolation location, and <code>2N</code> is the number of original data points.</p>
<p>
If the <CODE>COS&SIN</CODE> keyword is used, then the
<CODE>FFT</CODE> function returns the actual Fourier
coefficients. Let the cosine coefficients be called
<img src="fftI01.png"> 's and the sine coefficients be called
<img src="fftI02.png"> 's. <img src="fftI03.png"> is
the mean value of the input data. As shown in the example below, these
coefficients can be used for smooth interpolation. Suppose <img src="fftI04.png">
is the interpolation location, and <code>2N</code> is the number of original data
points.</p>
<p>
<center><img src="fftI05.png"></center></p>
<P>
<a href="fft.htm"><img align="top" border="0" src="../shadow_left.gif">
<font size="+1" color="olive">Fast Fourier transform</font></a><br />
<a href="fftS02.htm"><img align="top" border="0" src="../shadow_right.gif">
<font size="+1" color="olive">Discrete Fourier series</font></a>
</P>
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