Editing Revisiting SEP tour with Madagascar and SCons (section)

===Resampling===
The next example demonstrated simple signal processing using the Fast Fourier
Transform. We will first subsample the original data and then recover the data
using Fourier interpolation.
Subsampling is accomplished with <tt>sfwindow</tt>.
<syntaxhighlight lang="python">
# decimate time axis by two
Flow('subsampled','windowed','window j1=2')
</syntaxhighlight>

Running <tt>scons -Q subsampled.rsf</tt> produces
<pre>
< windowed.rsf /path/to/RSF/bin/sfwindow j1=2 > subsampled.rsf
</pre>
We can verify that the size of the first axis has decreased by running
<pre>
sfin windowed.rsf subsampled.rsf. 
</pre>
Try also <tt>sfwiggle < subsampled.rsf | sfpen</tt> to quickly inspect the subsampled data on the screen.
To interpolate the data back to the original sampling, the following sequence
of steps can be applied:
  
#Fourier transform from time domain to frequency domain. 
#Pad the frequency axis 
#Inverse Fourier transform from frequency to time. 
All three steps are conveniently combined into one using pipes.
<syntaxhighlight lang="python">
# sinc interpolation in the Fourier domain
Flow('resampled','subsampled',
     'fft1 | pad n1=102 | fft1 inv=y opt=n | window max1=0.8')
</syntaxhighlight>

Why do we pad the Fourier domain to 102? The time length of the original data
is 201 samples. In the frequency domain, it can be represented with 101
positive frequencies plus the zero frequency, which amounts to 102. Note that
the output of <tt>sffft1</tt> does not contain negative frequencies.
Finally, we display the result. The reconstructed data is shown in
the figure. Comparing this result with
the previous plots, we can verify a fairly accurate reconstruction.
<syntaxhighlight lang="python">
Result('resampled','wiggle title=Resampled' + plotpar)
</syntaxhighlight>

[[Image:resampled.png|frame|center|To see this figure on your screen, run <tt>scons resampled.view</tt>]] 

As an exercise, try subsampling the data by a factor of 4 and see if you can
still reconstruct the original data with the Fourier method.