From: <Saved by Windows Internet Explorer 7>
Subject: The Wavelet Transform
Date: Sun, 21 Dec 2008 12:08:21 -0600
MIME-Version: 1.0
Content-Type: multipart/related;
	type="text/html";
	boundary="----=_NextPart_000_0123_01C96364.D104C540"
X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3350

This is a multi-part message in MIME format.

------=_NextPart_000_0123_01C96364.D104C540
Content-Type: text/html;
	charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
Content-Location: http://www.eso.org/sci/data-processing/software/esomidas//doc/user/98NOV/volb/node308.html

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<!--Converted with LaTeX2HTML 98.1p1 release (March 2nd, 1998)=0A=
originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of =
Leeds=0A=
* revised and updated by:  Marcus Hennecke, Ross Moore, Herb Swan=0A=
* with significant contributions from:=0A=
  Jens Lippmann, Marek Rouchal, Martin Wilck and others =
--><HTML><HEAD><TITLE>The Wavelet Transform</TITLE>
<META content=3D"The Wavelet Transform" name=3Ddescription>
<META content=3Dvol2 name=3Dkeywords>
<META content=3Ddocument name=3Dresource-type>
<META content=3Dglobal name=3Ddistribution>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1"><LINK=20
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/vol2.css"=20
rel=3DSTYLESHEET><LINK href=3D"node370.html" rel=3Dnext><LINK =
href=3D"node307.html"=20
rel=3Dprevious><LINK href=3D"vol2.html" rel=3Dup><LINK =
href=3D"node309.html" rel=3Dnext>
<META content=3D"MSHTML 6.00.6000.16762" name=3DGENERATOR></HEAD>
<BODY><!--Navigation Panel--><A=20
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node309.html"=20
name=3Dtex2html5252><IMG height=3D24 alt=3Dnext=20
src=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/user=
/98NOV/volb/icons.gif/next_motif.gif"=20
width=3D37 align=3Dbottom border=3D0></A> <A=20
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/vol2.html"=20
name=3Dtex2html5249><IMG height=3D24 alt=3Dup=20
src=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/user=
/98NOV/volb/icons.gif/up_motif.gif"=20
width=3D26 align=3Dbottom border=3D0></A> <A=20
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node307.html"=20
name=3Dtex2html5243><IMG height=3D24 alt=3Dprevious=20
src=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/user=
/98NOV/volb/icons.gif/previous_motif.gif"=20
width=3D63 align=3Dbottom border=3D0></A> <A=20
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node1.html"=20
name=3Dtex2html5251><IMG height=3D24 alt=3Dcontents=20
src=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/user=
/98NOV/volb/icons.gif/contents_motif.gif"=20
width=3D65 align=3Dbottom border=3D0></A> <BR><B>Next:</B> <A=20
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node309.html"=20
name=3Dtex2html5253>Introduction</A> <B>Up:</B> <A=20
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/vol2.html"=20
name=3Dtex2html5250>No Title</A> <B>Previous:</B> <A=20
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node307.html"=20
name=3Dtex2html5244>Bibliography</A> <BR><BR><!--End of Navigation =
Panel-->
<H1><A name=3DSECTION002000000000000000000>The Wavelet Transform</A> =
</H1>
<P><BR>
<HR>
<!--Table of Child-Links--><A name=3DCHILD_LINKS>&nbsp;</A>=20
<UL>
  <LI><A=20
  =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node309.html"=20
  name=3Dtex2html5254>Introduction</A>=20
  <LI><A=20
  =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node310.html"=20
  name=3Dtex2html5255>The continuous wavelet transform</A>=20
  <LI><A=20
  =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node311.html"=20
  name=3Dtex2html5256>Examples of Wavelets</A>=20
  <UL>
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node312.html"=20
    name=3Dtex2html5257>Morlet's Wavelet</A>=20
    <UL>
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node313.html"=20
      name=3Dtex2html5258>Mexican Hat</A> </LI></UL></LI></UL>
  <LI><A=20
  =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node314.html"=20
  name=3Dtex2html5259>The discrete wavelet transform</A>=20
  <UL>
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node315.html"=20
    name=3Dtex2html5260>Introduction</A>=20
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node316.html"=20
    name=3Dtex2html5261>Multiresolution Analysis</A>=20
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node317.html"=20
    name=3Dtex2html5262>The <EM>=E0 trous</EM> algorithm </A>
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node318.html"=20
    name=3Dtex2html5263>Pyramidal Algorithm</A>=20
    <UL>
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node319.html"=20
      name=3Dtex2html5264>The Laplacian Pyramid</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node320.html"=20
      name=3Dtex2html5265>Pyramidal Algorithm with one Wavelet</A> =
</LI></UL>
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node321.html"=20
    name=3Dtex2html5266>Multiresolution with scaling functions with a =
frequency=20
    cut-off</A>=20
    <UL>
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node322.html"=20
      name=3Dtex2html5267>The Wavelet transform using the Fourier =
transform</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node323.html"=20
      name=3Dtex2html5268>The Reconstruction</A> </LI></UL></LI></UL>
  <LI><A=20
  =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node324.html"=20
  name=3Dtex2html5269>Visualization of the Wavelet Transform</A>=20
  <UL>
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node325.html"=20
    name=3Dtex2html5270>Visualisation of the first class</A>=20
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node326.html"=20
    name=3Dtex2html5271>Visualisation of the second class</A>=20
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node327.html"=20
    name=3Dtex2html5272>Visualisation of the third class</A> </LI></UL>
  <LI><A=20
  =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node328.html"=20
  name=3Dtex2html5273>Noise reduction from the wavelet transform</A>=20
  <UL>
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node329.html"=20
    name=3Dtex2html5274>The convolution from the continuous wavelet =
transform</A>=20
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node330.html"=20
    name=3Dtex2html5275>The Wiener-like filtering in the wavelet =
space</A>=20
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node331.html"=20
    name=3Dtex2html5276>Hierarchical Wiener filtering</A>=20
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node332.html"=20
    name=3Dtex2html5277>Adaptive filtering from the wavelet =
transform</A>=20
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node333.html"=20
    name=3Dtex2html5278>Hierarchical adaptive filtering</A> </LI></UL>
  <LI><A=20
  =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node334.html"=20
  name=3Dtex2html5279>Comparison using a multiresolution quality =
criterion</A>=20
  <LI><A=20
  =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node335.html"=20
  name=3Dtex2html5280>Deconvolution</A>=20
  <UL>
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node336.html"=20
    name=3Dtex2html5281>Introduction</A>=20
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node337.html"=20
    name=3Dtex2html5282>Regularization in the wavelet space</A>=20
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node338.html"=20
    name=3Dtex2html5283>Tikhonov's regularization and multiresolution =
analysis</A>=20

    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node339.html"=20
    name=3Dtex2html5284>Regularization from significant structures</A>=20
    <UL>
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node340.html"=20
      name=3Dtex2html5285>Regularization of Van Cittert's algorithm</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node341.html"=20
      name=3Dtex2html5286>Regularization of the one-step gradient =
method</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node342.html"=20
      name=3Dtex2html5287>Regularization of Lucy's algorithm</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node343.html"=20
      name=3Dtex2html5288>Convergence</A> </LI></UL></LI></UL>
  <LI><A=20
  =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node344.html"=20
  name=3Dtex2html5289>The wavelet context in MIDAS</A>=20
  <UL>
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node345.html"=20
    name=3Dtex2html5290>Introduction</A>=20
    <LI><A=20
    =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node346.html"=20
    name=3Dtex2html5291>Commands Description</A>=20
    <UL>
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node347.html"=20
      name=3Dtex2html5292>TRANSF/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node348.html"=20
      name=3Dtex2html5293>RECONS/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node349.html"=20
      name=3Dtex2html5294>HEADER/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node350.html"=20
      name=3Dtex2html5295>INFO/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node351.html"=20
      name=3Dtex2html5296>EXTRAC/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node352.html"=20
      name=3Dtex2html5297>ENTER/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node353.html"=20
      name=3Dtex2html5298>VISUAL/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node354.html"=20
      name=3Dtex2html5299>VISUAL/CUB</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node355.html"=20
      name=3Dtex2html5300>VISUAL/CONT</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node356.html"=20
      name=3Dtex2html5301>VISUAL/SYNT</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node357.html"=20
      name=3Dtex2html5302>VISUAL/PLAN</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node358.html"=20
      name=3Dtex2html5303>VISUAL/PERS</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node359.html"=20
      name=3Dtex2html5304>FILTER/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node360.html"=20
      name=3Dtex2html5305>COMPAR/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node361.html"=20
      name=3Dtex2html5306>PLOT/SNR</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node362.html"=20
      name=3Dtex2html5307>PLOT/COR</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node363.html"=20
      name=3Dtex2html5308>DIRECT/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node364.html"=20
      name=3Dtex2html5309>CITTERT/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node365.html"=20
      name=3Dtex2html5310>GRAD/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node366.html"=20
      name=3Dtex2html5311>LUCY/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node367.html"=20
      name=3Dtex2html5312>TUTORIAL/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node368.html"=20
      name=3Dtex2html5313>TRAN1D/WAVE</A>=20
      <LI><A=20
      =
href=3D"http://www.eso.org/sci/data-processing/software/esomidas//doc/use=
r/98NOV/volb/node369.html"=20
      name=3Dtex2html5314>REC1D/WAVE</A> =
</LI></UL></LI></UL></LI></UL><!--End of Table of Child-Links--><BR>
<HR>

<ADDRESS><I>Petra Nass</I> <BR><I>1999-06-15</I> =
</ADDRESS></BODY></HTML>

------=_NextPart_000_0123_01C96364.D104C540
Content-Type: image/gif
Content-Transfer-Encoding: base64
Content-Location: http://www.eso.org/sci/data-processing/software/esomidas//doc/user/98NOV/volb/icons.gif/next_motif.gif

R0lGODdhJQAYAPEAAL+/v+fn529vb1sAACwAAAAAJQAYAAACfYyPqcvtv4QBtNqL8xUy6A9i3BSW
3+iZ6tZVA/auYksNsSsDN4Di+27a9Wo6y81mI/qSlGHx+fwpjxZnjHk1TnEVK/eKZOqkXRq0mM2I
z16f8pJmm4FiapTbnMN/WO24TJKj4iRYQlgIcoioobg4Y8ARKTlJWWkZYJmpmVkAADs=

------=_NextPart_000_0123_01C96364.D104C540
Content-Type: image/gif
Content-Transfer-Encoding: base64
Content-Location: http://www.eso.org/sci/data-processing/software/esomidas//doc/user/98NOV/volb/icons.gif/up_motif.gif

R0lGODdhGgAYAPEAAL+/v+fn529vb1sAACwAAAAAGgAYAAACYoyPqcutYoCctFogYLj85tiF0reJ
ITkNlnpq6SqiEkvRnAzY8z70FK7LzVg2IEz4Grl2FWJtYmwyp9EnkrqcXn1XTHbI5YW9IFFQWQ6d
ySXz7Wuy4OJyTeaOz+vxgb3/L1AAADs=

------=_NextPart_000_0123_01C96364.D104C540
Content-Type: image/gif
Content-Transfer-Encoding: base64
Content-Location: http://www.eso.org/sci/data-processing/software/esomidas//doc/user/98NOV/volb/icons.gif/previous_motif.gif

R0lGODdhPwAYAPEAAL+/v+fn529vb1sAACwAAAAAPwAYAAACrYyPqcvtD6OcSRiAs968+w9qghWE
5ol+45W2LriW70wDcTbkeo0NvEjCaXK/IubW2/iMPyRgKXxKe7upEKrDDqnEjBP6XHatU61VHE2C
od+sORk1o+NbMJBF3uLc8HLffzXmFfSnV3hFl/hXZUOYl/aopgh4yOZoB3lmqMkZRmaJh1kp+Lkn
uCPG2IjH1DrI6trqFCvrSMs0e1sUM9Lr+wscLDxMHBxQjJysjFwAADs=

------=_NextPart_000_0123_01C96364.D104C540
Content-Type: image/gif
Content-Transfer-Encoding: base64
Content-Location: http://www.eso.org/sci/data-processing/software/esomidas//doc/user/98NOV/volb/icons.gif/contents_motif.gif

R0lGODdhQQAYAPEAAL+/v+fn529vb1sAACwAAAAAQQAYAAACsoyPqcvtD6OcTRiAs968+w9yghWE
5omG45W2rrmW70xn8TbkQ81/d5YDznYvoo+kMWKUKGZThVyCdMadbhnEZgHW7JX7xfy4UylWSDab
t8R20hZNd5RudPUtT9dFcSd6jVdFtaenxceShxO4qIYHmLQ1lkhIqeZH1/gnycaYV/n4iCkWp8VE
9adHx2nXFgYg2RMLAitbu0Frm4ubW7vLGxszIjxMXGx8jJyMHKDc7Pz8XAAAOw==

------=_NextPart_000_0123_01C96364.D104C540
Content-Type: text/css;
	charset="iso-8859-1"
Content-Transfer-Encoding: 7bit
Content-Location: http://www.eso.org/sci/data-processing/software/esomidas//doc/user/98NOV/volb/vol2.css

.MATH {
	FONT-FAMILY: "Century Schoolbook", serif
}
.MATH I {
	FONT-WEIGHT: bold; FONT-FAMILY: "Century Schoolbook", serif
}
.BOLDMATH {
	FONT-WEIGHT: bold; FONT-FAMILY: "Century Schoolbook", serif
}
SMALL.XTINY {
	FONT-SIZE: xx-small
}
SMALL.TINY {
	FONT-SIZE: x-small
}
SMALL.SCRIPTSIZE {
	FONT-SIZE: smaller
}
SMALL.FOOTNOTESIZE {
	FONT-SIZE: small
}
SMALL.SMALL {
	
}
BIG.LARGE {
	
}
BIG.XLARGE {
	FONT-SIZE: large
}
BIG.XXLARGE {
	FONT-SIZE: x-large
}
BIG.HUGE {
	FONT-SIZE: larger
}
BIG.XHUGE {
	FONT-SIZE: xx-large
}

------=_NextPart_000_0123_01C96364.D104C540--