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<H2><A NAME="SECTION001745000000000000000"> </A><A NAME="s:cfou"> </A>
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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: $S(\nu) = |{\cal F}X^{(m)}|^2$ -->
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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>
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<ADDRESS>
<I>Petra Nass</I>
<BR><I>1999-06-15</I>
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