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  <name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Adaptive Echo Cancellation</name>
  <metadata xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
  <md:version xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">**new**</md:version>
  <md:created xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2003/07/10 11:30:34.413 GMT-5</md:created>
  <md:revised xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2003/08/05 15:03:49.171 GMT-5</md:revised>
  <md:authorlist xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
    <md:author xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="dljones">
      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Douglas</md:firstname>
      <md:othername xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">L.</md:othername>
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Jones</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">dl-jones@uiuc.edu</md:email>
    </md:author>
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      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Douglas</md:firstname>
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      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Jones</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">dl-jones@uiuc.edu</md:email>
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      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Kyle</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Clarkson</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">kclarks@rice.edu</md:email>
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  <md:abstract xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/"/>
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  <content xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
    <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="delete_me">
      An adaptive echo canceller is a specific type of adaptive interference
      canceller that removes echos. Adaptive echo
    cancellers are found in all modern telephone systems.
      <figure xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="figure1">
	<media xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" type="image/png" src="fig1AdaptiveEcho.png"/>
      </figure>
      The hybrid is supposed to split the opposite-going waves,
      but typically achieves only about 15dB of suppression. This signal will
      eventually reach the other end and be coupled back, with a long
      delay, to the original source, which gives a very annoying echo.
      
      <figure xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="figure2">
	<name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Echo canceller</name>
	<media xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" type="image/png" src="fig2AdaptiveEcho.png"/>
      </figure>
     
      Because the input to the adaptive echo canceller contains only
      the signal from the far end that will echo off of the hybrid,
      it cancels the echo while passing the near-end signal as desired.
    </para>
    <section xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="narrow">
      <name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Narrowband interference canceller</name>
      
      <figure xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="figure3">
	<media xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" type="image/png" src="fig3AdaptiveEcho.png"/>
      </figure>
      
      <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="para2">
	A sinusoid is predictable
	<m:math><m:ci>Δ</m:ci></m:math> samples ahead, whereas
	<m:math>
	  <m:ci>
	    <m:msub>
	      <m:mi>s</m:mi>
	      <m:mi>k</m:mi>
	    </m:msub>
	  </m:ci>
	</m:math> may not be, so the sinusoid can be cancelled using the
        adaptive system in the Figure.  This is another special case of the
        adaptive interference canceller in which the noise reference input
        is a delayed version of the primary (signal plus noise) input.
        Note that <m:math><m:ci>Δ</m:ci></m:math> must be large
	enough so that
	<m:math>
	  <m:ci>
	    <m:msub>
	      <m:mi>s</m:mi>
	      <m:mi>k</m:mi>
	    </m:msub>
	  </m:ci>
	</m:math>
        and
	<m:math>
	  <m:ci>
	    <m:msub>
	      <m:mi>s</m:mi>
	      <m:mrow>
		<m:mi>k</m:mi>
		<m:mo>-</m:mo>
		<m:mi>Δ</m:mi>
	      </m:mrow>
	    </m:msub>
	  </m:ci>
	</m:math> are uncorrelated, or some of the signal will be
	cancelled as well!
      </para>
      <exercise xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="ex1">
	<problem xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
	  <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="para4">
	    How would you construct an "adaptive line enhancer"
            that preserves the sinusoids but cancels the uncorrelated noise?
	  </para>
	</problem>
      </exercise>
      <list xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="list1" type="bulleted">
	<name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Other Applications</name>
	<item xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Adaptive array processing</item>
	<item xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Adaptive control</item>
	<item xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">etc...</item>
      </list>
    </section>
  </content>
  
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