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<document xmlns="http://cnx.rice.edu/cnxml" 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="new11">
  <name>Adaptive Echo Cancellation</name>
  <metadata>
  <md:version>**new**</md:version>
  <md:created>2003/07/10 11:30:34.413 GMT-5</md:created>
  <md:revised>2003/08/05 15:03:49.171 GMT-5</md:revised>
  <md:authorlist>
    <md:author id="dljones">
      <md:firstname>Douglas</md:firstname>
      <md:othername>L.</md:othername>
      <md:surname>Jones</md:surname>
      <md:email>dl-jones@uiuc.edu</md:email>
    </md:author>
  </md:authorlist>

  <md:maintainerlist>
    <md:maintainer id="dljones">
      <md:firstname>Douglas</md:firstname>
      <md:othername>L.</md:othername>
      <md:surname>Jones</md:surname>
      <md:email>dl-jones@uiuc.edu</md:email>
    </md:maintainer>
    <md:maintainer id="kclarks">
      <md:firstname>Kyle</md:firstname>
      
      <md:surname>Clarkson</md:surname>
      <md:email>kclarks@rice.edu</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  

  <md:abstract/>
</metadata>

  <content>
    <para 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 id="figure1">
	<media 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 id="figure2">
	<name>Echo canceller</name>
	<media 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 id="narrow">
      <name>Narrowband interference canceller</name>
      
      <figure id="figure3">
	<media type="image/png" src="fig3AdaptiveEcho.png"/>
      </figure>
      
      <para 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 id="ex1">
	<problem>
	  <para id="para4">
	    How would you construct an "adaptive line enhancer"
            that preserves the sinusoids but cancels the uncorrelated noise?
	  </para>
	</problem>
      </exercise>
      <list id="list1" type="bulleted">
	<name>Other Applications</name>
	<item>Adaptive array processing</item>
	<item>Adaptive control</item>
	<item>etc...</item>
      </list>
    </section>
  </content>
  
</document>
