testing-out-analytic-filter-functions.html

<!DOCTYPE html>
<html lang="en">
<link rel="stylesheet" type="text/css" href="https://keflavich.github.io/blog/theme/css/style.css" />
<link rel="icon" type="image/gif" href="https://keflavich.github.io/blog/theme/favicon8.ico">
<head>
    <base href="https://keflavich.github.io/blog">
        <title>Adam Ginsburg's blog</title>
        <meta charset="utf-8" />
        <link href="https://keflavich.github.io/blog/feeds/all.atom.xml" type="application/atom+xml" rel="alternate" title="Adam Ginsburg's blog Full Atom Feed" />
        <link href="https://keflavich.github.io/blog/feeds/{slug}.atom.xml" type="application/atom+xml" rel="alternate" title="Adam Ginsburg's blog Categories Atom Feed" />
<!-- Using MathJax, with the delimiters $ -->
<!-- Conflict with pygments for the .mo and .mi -->
<script type="text/x-mathjax-config">
    MathJax.Hub.Config({
    "HTML-CSS": {
    styles: {
    ".MathJax .mo, .MathJax .mi": {color: "inherit !important"}},
    'div.typeset': { 'text-align': 'left'}
    },
    tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']],processEscapes: true}
    });
    TeX: {
        extensions: ["AMSmath.js", "AMSsymbols.js"]
    }
    MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function () {
    var VARIANT = MathJax.OutputJax["HTML-CSS"].FONTDATA.VARIANT;
    VARIANT["normal"].fonts.unshift("MathJax_SansSerif");
    VARIANT["bold"].fonts.unshift("MathJax_SansSerif-bold");
    VARIANT["italic"].fonts.unshift("MathJax_SansSerif-italic");
    VARIANT["-tex-mathit"].fonts.unshift("MathJax_SansSerif-italic");
    });
    MathJax.Hub.Register.StartupHook("SVG Jax Ready",function () {
    var VARIANT = MathJax.OutputJax.SVG.FONTDATA.VARIANT;
    VARIANT["normal"].fonts.unshift("MathJax_SansSerif");
    VARIANT["bold"].fonts.unshift("MathJax_SansSerif-bold");
    VARIANT["italic"].fonts.unshift("MathJax_SansSerif-italic");
    VARIANT["-tex-mathit"].fonts.unshift("MathJax_SansSerif-italic");
    });
</script>

<script type="text/javascript"
src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML">
</script>
        
</head>

<body id="base" class="home">


    <header id="banner" class="body" >
        <div id="header" style='background-image: url("https://keflavich.github.io/blog/images/GC_4096sq_bolo.png"); background-position:left; min-heigt: 200px;  background-repeat: no-repeat; max-width: 80%;'>
            <h1 style="color: #C4C4C4;"><a class="header" href="https://keflavich.github.io/blog">Adam Ginsburg's blog <strong></strong></a></h1>

            <nav id="menu"><ul id="menulist">
                <li><a href="https://www.adamgginsburg.com">Homepage</a></li>
                <li><a href="/blog//index.html">Blog Index</a></li>
                <li><a href="/blog//blog/category/bgps.html">BGPS Blog</a></li>
                <li><a href="/blog//blog/category/publications.html">Publications</a></li>
                <li><a href="/blog//blog/archives.html">Archives</a></li>
                <li><a href="/blog//blog/tags.html">Tags</a></li>
            </ul></nav><!-- /#menu -->
        </div>
    </header><!-- /#banner -->

  <div id="sidebar">
    <ul>
      <li>
        <h3 id='recent_header'>Recent Posts</h3>
        <ul>
              <li class="post">
                  2025/03/15
                  <br>
                  <a href="https://keflavich.github.io/blog/pushing-to-a-pull-request.html">Pushing to a pull request</a>
              </li>
              <li class="post">
                  2023/08/11
                  <br>
                  <a href="https://keflavich.github.io/blog/editing-metadata-in-measurement-sets.html">Editing metadata in measurement sets</a>
              </li>
              <li class="post">
                  2022/05/06
                  <br>
                  <a href="https://keflavich.github.io/blog/casa-mpi-debugging-contd.html">CASA MPI debugging cont'd</a>
              </li>
              <li class="post">
                  2022/05/01
                  <br>
                  <a href="https://keflavich.github.io/blog/co2-monitoring-at-conferences-update-in-2022.html">CO2 Monitoring at Conferences: Update in 2022</a>
              </li>
              <li class="post">
                  2022/04/14
                  <br>
                  <a href="https://keflavich.github.io/blog/alma-cycle-9-corrupted-zip-fix.html">ALMA Cycle 9 corrupted zip fix</a>
              </li>
        </ul>
      </li>
    
    </ul>
  </div><!-- end #sidebar -->

  <div id="content">
<section id="content" class="body">
  <header>
    <h2 class="entry-title">
      <a href="https://keflavich.github.io/blog/testing-out-analytic-filter-functions.html" rel="bookmark"
         title="Permalink to Testing out analytic filter functions">Testing out analytic filter functions</a></h2>
 
  </header>
  <footer class="post-info">
    <abbr class="published" title="2011-07-15T03:03:00-06:00">
      2011/07/15
    </abbr>
    <address class="vcard author">
      By <a class="url fn" href="https://keflavich.github.io/blog/author/adam-adamgginsburggmailcom.html">Adam (adam.g.ginsburg@gmail.com)</a>
    </address>
  </footer><!-- /.post-info -->
  <div class="entry-content">
    <p>I've attempted to model the spatial filter function as a gaussian (or
PSF) plus an inverse gaussian. i.e., the high-spatial-frequency
components are smoothed with the PSF, and the low spatial frequency
components are convolved with a (1-gaussian) high-pass filter.
First, the mildly good news: With a 300&quot; FWHM large-scale cutoff, the
filter PSD reasonably resembles the iterative map PSD:</p>
<img alt="" src="http://3.bp.blogspot.com/-udANxY5rM98/Th-i7hx3qnI/AAAAAAAAGS0/kwoR30ZO5OI/s320/exp12_ds2_astrosky_arrang45_atmotest_amp5.0E%252B02_sky00_seed00_peak050.00_nosmooth_map20filterpsds.png" />
<p>Luckily, the double-filter goes a very long way in explaining the
scale-free flux loss. In the following diagram, I show the effect of the
filter compared to the input map.</p>
<img alt="" src="http://3.bp.blogspot.com/-iZtSoQjlzJY/Th-jf6oatlI/AAAAAAAAGS8/p8ZcznsKGpI/s320/exp12_ds2_astrosky_arrang45_atmotest_amp5.0E%252B02_sky00_seed00_peak050.00_nosmooth_filterpsds.png" />
<p>The filter only recovers about 75% of the flux at ANY wavenumber. The
map does slightly worse at high frequencies, which I can't explain yet.
These show the recovery fraction of the iterative maps, a gaussian
smoothing function with FWHM=33&quot;, and the mid-pass-filter. Map20 (no
smooth) has a lot of additional &quot;noise power&quot; at high spatial
frequencies; if it wasn't for the telescope filter function, we would
apparently have pretty good high-frequency recovery. Hmph.
Note that map20 is higher than the filter at some intermediate
frequencies, but quite a bit lower at higher frequencies. Also note the
moderately poor agreement between the 'smoothed' and 'smoothed (theory)'
lines.</p>
<img alt="" src="http://4.bp.blogspot.com/-zhxfyI_XDNY/Th-qZmsMZaI/AAAAAAAAGTE/550ocw2kFx8/s320/filterfunctions_smoothedx2.png" />
<p>Finally, look at the comparison between map20 and fiiltered. The
agreement is not bad for positive points; filtered is apparently
slightly higher but that can be adjusted. The problem: the filter forces
some structures that are negative or zero to be positive. For example,
look at the feature at 210,300 that is negative in Map20 but positive in
Filtered. In the real (input) map, this feature is lower than its
surroundings - it is legitimately negative.</p>
<img alt="" src="http://4.bp.blogspot.com/-zH98yuBL7lo/Th-tQIoKYCI/AAAAAAAAGTM/QNqslST6b2c/s320/exp12_ds2_astrosky_arrang45_atmotest_amp5.0E%252B02_sky00_seed00_peak050.00_nosmooth_map20filtercompare.png" />
<img alt="" src="http://2.bp.blogspot.com/-bvlju06_ySU/Th-ttpCOuhI/AAAAAAAAGTU/3zoCyl5gCIY/s320/exp12_ds2_astrosky_arrang45_atmotest_amp5.0E%252B02_sky00_seed00_peak050.00_nosmooth_filtercompare.png" />

  </div><!-- /.entry-content -->
</section>

  </div>

    <script type="text/javascript">
    var _gaq = _gaq || [];
    _gaq.push(['_setAccount', 'UA-37306139-1']);
    _gaq.push(['_trackPageview']);
    (function() {
        var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true;
        ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
        var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s);
    })();

    (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
    (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
    m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
    })(window,document,'script','//www.google-analytics.com/analytics.js','ga');

    ga('create', 'UA-37306139-1');
    ga('send', 'pageview');
</script>
<!-- Start of StatCounter Code for Default Guide -->
<script type="text/javascript">
var sc_project=9280906; 
var sc_invisible=1; 
var sc_security="7107d360"; 
var scJsHost = (("https:" == document.location.protocol) ?
"https://secure." : "http://www.");
document.write("<sc"+"ript type='text/javascript' src='" +
scJsHost+
"statcounter.com/counter/counter.js'></"+"script>");
</script>
<!--<noscript><div class="statcounter"><a title="hit counter"
href="http://statcounter.com/free-hit-counter/"
target="_blank"><img class="statcounter"
src="http://c.statcounter.com/9280906/0/7107d360/1/"
alt="hit counter"></a></div></noscript>-->
<!-- End of StatCounter Code for Default Guide -->
<script type="text/javascript">
  var disqus_shortname = 'adamginsburgsblog';
  var disqus_identifier = '/testing-out-analytic-filter-functions.html';
  var disqus_url = 'https://keflavich.github.io/blog/testing-out-analytic-filter-functions.html';
  var disqus_title = 'Testing out analytic filter functions';
  (function() {
        var dsq = document.createElement('script'); dsq.type = 'text/javascript'; dsq.async = true;
        dsq.src = 'https://' + disqus_shortname + '.disqus.com/embed.js';
        (document.getElementsByTagName('head')[0] || document.getElementsByTagName('body')[0]).appendChild(dsq);
   })();
</script>
</body>
</html>