2022-04-12 22:02:59 -03:00
|
|
|
<!DOCTYPE html>
|
2022-04-12 21:54:18 -03:00
|
|
|
|
|
|
|
<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
|
|
|
|
original version by: Nikos Drakos, CBLU, University of Leeds
|
|
|
|
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
|
|
|
* with significant contributions from:
|
|
|
|
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
|
|
|
|
<HTML>
|
|
|
|
<HEAD>
|
2022-04-12 22:02:59 -03:00
|
|
|
|
|
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
|
|
|
|
|
|
|
|
2022-04-12 21:54:18 -03:00
|
|
|
<TITLE>Properties of Fourier transforms</TITLE>
|
|
|
|
<META NAME="description" CONTENT="Properties of Fourier transforms">
|
|
|
|
<META NAME="keywords" CONTENT="book">
|
|
|
|
<META NAME="resource-type" CONTENT="document">
|
|
|
|
<META NAME="distribution" CONTENT="global">
|
|
|
|
|
|
|
|
<META NAME="Generator" CONTENT="LaTeX2HTML v2002-2-1">
|
|
|
|
<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
|
|
|
|
|
|
|
|
<LINK REL="STYLESHEET" HREF="book.css">
|
|
|
|
|
|
|
|
<LINK REL="next" HREF="node171.html">
|
|
|
|
<LINK REL="previous" HREF="node164.html">
|
|
|
|
<LINK REL="up" HREF="node163.html">
|
|
|
|
<LINK REL="next" HREF="node168.html">
|
|
|
|
</HEAD>
|
|
|
|
|
|
|
|
<BODY >
|
|
|
|
<!--Navigation Panel-->
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html3073"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node168.html">
|
|
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="next.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html3067"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node163.html">
|
|
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="up.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html3061"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node166.html">
|
|
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="prev.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html3069"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node4.html">
|
|
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="contents.png"></A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="tex2html3071"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node201.html">
|
|
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="index.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<BR>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Next:</B> <A ID="tex2html3074"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node168.html">Fourier transform of DC</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Up:</B> <A ID="tex2html3068"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node163.html">Fourier analysis and resynthesis</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> Previous:</B> <A ID="tex2html3062"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node166.html">Fourier transform as additive</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> <A ID="tex2html3070"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node4.html">Contents</A></B>
|
2022-04-12 23:32:40 -03:00
|
|
|
<B> <A ID="tex2html3072"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node201.html">Index</A></B>
|
|
|
|
<BR>
|
|
|
|
<BR>
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
2022-04-12 23:32:40 -03:00
|
|
|
<H1><A ID="SECTION001320000000000000000">
|
2022-04-12 21:54:18 -03:00
|
|
|
Properties of Fourier transforms</A>
|
|
|
|
</H1>
|
|
|
|
|
|
|
|
<P>
|
|
|
|
In this section we will investigate what happens when we take the Fourier
|
2022-04-12 23:17:03 -03:00
|
|
|
transform of a (complex) sinusoid. The simplest one is "DC", the special
|
2022-04-12 21:54:18 -03:00
|
|
|
sinusoid of frequency zero. After we derive the Fourier transform of that, we
|
|
|
|
will develop some properties of Fourier transforms that allow us to apply the
|
|
|
|
result to any other sinusoid.
|
|
|
|
|
|
|
|
<P>
|
|
|
|
<BR><HR>
|
|
|
|
<!--Table of Child-Links-->
|
2022-04-12 23:32:40 -03:00
|
|
|
<A ID="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
|
|
|
|
<UL>
|
2022-04-12 23:32:40 -03:00
|
|
|
<LI><A ID="tex2html3075"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node168.html">Fourier transform of DC</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<LI><A ID="tex2html3076"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node169.html">Shifts and phase changes</A>
|
2022-04-12 23:32:40 -03:00
|
|
|
<LI><A ID="tex2html3077"
|
2022-04-12 21:54:18 -03:00
|
|
|
HREF="node170.html">Fourier transform of a sinusoid</A>
|
|
|
|
</UL>
|
|
|
|
<!--End of Table of Child-Links-->
|
|
|
|
<BR><HR>
|
|
|
|
<ADDRESS>
|
|
|
|
Miller Puckette
|
|
|
|
2006-12-30
|
|
|
|
</ADDRESS>
|
|
|
|
</BODY>
|
|
|
|
</HTML>
|