1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
|
<HTML>
<HEAD>
<TITLE>Fast Fourier transform</TITLE>
</HEAD>
<BODY bgcolor="#FFFFFF" fgcolor="#000000">
<P><font size="+3" color="green"><B>Fast Fourier transform</B></font></P>
<P>
<TABLE border="1" cols="2" frame="box" rules="all" width="572">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%"><CODE>
m = FFT(y)<br />
m = FFT(y,'AMP&PHASE')<br />
m = FFT(y,'COS&SIN')</CODE>
</TD></TR>
</table></p>
<p>
The <CODE>FFT</CODE> function calculates the
discrete fast Fourier transform of the input variable,
<CODE>y</CODE>. By default, <CODE>FFT</CODE> returns the amplitudes and
the phases, where the phases are in degrees. If the
<CODE>COS&SIN</CODE> keyword is used, <CODE>FFT</CODE> returns the Fourier
coefficients.</p>
<p>
Note that the reason that the amplitudes and phases are returned by
default is historical. Actually, the Fourier coefficients, that is, the
cosine and sine coefficients, are calculated and the amplitudes and
phases are just derived from them, as described below. It is a
simple matter for the user to request the cosine and sine coefficients,
and then to calculate the amplitudes and phases him/herself.</p>
<p>
Suppose that the length of the input vector is <code>2N</code>. The
output of this function is a matrix with <code>N+1</code> rows and 2
columns. The first column contains the amplitudes (or the cosine
coefficients), and the second column contains the phases (or the sine
coefficients).</p>
<p>
The <CODE><a href="ifft.htm">IFFT</a></CODE> function
calculates the inverse fast Fourier transform.</p>
<p>
<a href="fftS01.htm"><font size="+1" color="olive">Fourier coefficients</font></a><br />
<a href="fftS02.htm"><font size="+1" color="olive">Discrete Fourier series</font></a><br />
<a href="fftS03.htm"><font size="+1" color="olive">Restrictions</font></a><br />
<a href="fftS04.htm"><font size="+1" color="olive">Prime factors</font></a><br />
<a href="fftS05.htm"><font size="+1" color="olive">Example</font></a></p>
</BODY>
</HTML>
|
