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<HTML>
<HEAD>
<TITLE>Example</TITLE>
</HEAD>
<BODY bgcolor="#FFFFFF" fgcolor="#000000">
<p>
<font size="+1" color="green"><B>Example</B></font></P>
<p>
The following script demonstrates how you can use the <code>FFT</code>
function to smooth data. Note that when all the Fourier coefficients are used, the smoothed
curve must pass through the original data points.</p>
<p>
<font color="blue"><pre>
PI = ACOS(-1) ! define pi
N = 16 ! even number of points
X = [0:N-1]*2*PI/N ! generate some "data"
Y = SIN(X)+5*RAN(X) !
M = FFT(Y,'COS&SIN') ! calculate Fourier coefficients
H = M[*,1] ! extract column 1 as a vector
G = M[*,2] ! extract column 2 as a vector
Z = [0:2*PI:.05]
DO J = [3:N/2+1:2]
WINDOW (J-3)/2+5 ! choose a graphics window
SCALE 0 6 0 -2 7 0 ! set axis scales
SET PLOTSYMBOL -1 ! choose plotting symbol
SET %XNUMBERHEIGHT 5
SET %YNUMBERHEIGHT 5
GRAPH X Y ! plot original data
SET PLOTSYMBOL 0 ! choose no plotting symbol
VECTOR TMP len(z)
DO K = [2:J]
TMP = TMP + H[K]*COS((K-1)*Z)+G[K]*SIN((K-1)*Z)
ENDDO
GRAPH/OVERLAY Z H[1]/2+TMP
destroy tmp
SET %TEXTHEIGHT 5 ! increase the size of the text label
SET %XTEXTLOCATION 50
SET %YTEXTLOCATION 85
SET TEXTALIGN 2
SET TEXTINTERACTIVE 0
TEXT RCHAR(J)//' harmonics used'
ENDDO
GRAPH/OVERLAY [0;2*PI] [H[1]/2;H[1]/2] ! overlay the mean value
CLEAR/-REPLOT
REPLOT/ALL
</pre></font></p>
<p>
<center><img src="fftS05I01.jpg"></center></p>
<P>
<a href="fftS04.htm"><img align="top" border="0" src="../shadow_left.gif">
<font size="+1" color="olive">Prime factors</font></a></p>
</BODY>
</HTML>
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