<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <!--Converted with LaTeX2HTML 98.1p1 release (March 2nd, 1998) originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), 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> <TITLE>Fourier analysis</TITLE> <META NAME="description" CONTENT="Fourier analysis"> <META NAME="keywords" CONTENT="vol2"> <META NAME="resource-type" CONTENT="document"> <META NAME="distribution" CONTENT="global"> <META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"> <LINK REL="STYLESHEET" HREF="vol2.css"> <LINK REL="next" HREF="node241.html"> <LINK REL="previous" HREF="node239.html"> <LINK REL="up" HREF="node235.html"> <LINK REL="next" HREF="node241.html"> </HEAD> <BODY > <!--Navigation Panel--> <A NAME="tex2html4398" HREF="node241.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="icons.gif/next_motif.gif"></A> <A NAME="tex2html4395" HREF="node235.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="icons.gif/up_motif.gif"></A> <A NAME="tex2html4389" HREF="node239.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="icons.gif/previous_motif.gif"></A> <A NAME="tex2html4397" HREF="node1.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="icons.gif/contents_motif.gif"></A> <BR> <B> Next:</B> <A NAME="tex2html4399" HREF="node241.html">Time series analysis in</A> <B> Up:</B> <A NAME="tex2html4396" HREF="node235.html">MIDAS utilities for time</A> <B> Previous:</B> <A NAME="tex2html4390" HREF="node239.html">Output data format</A> <BR> <BR> <!--End of Navigation Panel--> <H2><A NAME="SECTION001745000000000000000"> </A><A NAME="s:cfou"> </A> <BR> Fourier analysis </H2> <P> Because of its universal relevance, it is recommended to always start the analysis by computing the power spectrum. However, since the power spectrum is not the optimal method for quite a number of TSA applications, other methods should always be tried thereafter. <P> <DL> <DT><STRONG><TT>POWER/TSA</TT> -</STRONG> <DD><B>Power spectrum:</B> This command computes the discrete power spectrum for unevenly sampled data a by relatively slow method. The discrete Fourier power spectrum (cf., e.g., Deeming, 1975) corresponds to a pure sinewave model and has basic significance in time series analysis. The corresponding test statistic is <!-- MATH: $S(\nu) = |{\cal F}X^{(m)}|^2$ --> <IMG WIDTH="122" HEIGHT="48" ALIGN="MIDDLE" BORDER="0" SRC="img529.gif" ALT="$S(\nu) = \vert{\cal F}X^{(m)}\vert^2$">. Because the statistic is the sum of the squares of two generally correlated variables for sine and cosine, it has has no known statistical properties. Therefore, we recommend to use other statistics for a more reliable signal detection and evaluation. <P> One of the important applications of the power spectrum analysis is the computation of the window function in order to evaluate the sampling pattern. For this particular application, set all data values in column <TT>:VALUE</TT> to 1 (for instance by using <TT>COMPUTE/TABLE</TT>) and then apply <TT>POWER/TSA</TT>. The resulting power spectrum is the window function of the data set. </DL> <P> <HR> <!--Navigation Panel--> <A NAME="tex2html4398" HREF="node241.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="icons.gif/next_motif.gif"></A> <A NAME="tex2html4395" HREF="node235.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="icons.gif/up_motif.gif"></A> <A NAME="tex2html4389" HREF="node239.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="icons.gif/previous_motif.gif"></A> <A NAME="tex2html4397" HREF="node1.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="icons.gif/contents_motif.gif"></A> <BR> <B> Next:</B> <A NAME="tex2html4399" HREF="node241.html">Time series analysis in</A> <B> Up:</B> <A NAME="tex2html4396" HREF="node235.html">MIDAS utilities for time</A> <B> Previous:</B> <A NAME="tex2html4390" HREF="node239.html">Output data format</A> <!--End of Navigation Panel--> <ADDRESS> <I>Petra Nass</I> <BR><I>1999-06-15</I> </ADDRESS> </BODY> </HTML>