<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE document PUBLIC "-//CNX//DTD CNXML 0.5 plus MathML//EN" "http://cnx.rice.edu/cnxml/0.5/DTD/cnxml_mathml.dtd">
<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="None">
  <name>Signals, Systems and Transforms:  Matching Problems</name>
  <metadata>
  <md:version>**new**</md:version>
  <md:created>2004/09/22 15:05:28.884 GMT-5</md:created>
  <md:revised>2004/09/22 15:07:46.228 GMT-5</md:revised>
  <md:authorlist>
      <md:author id="selesi">
      <md:firstname>Ivan</md:firstname>
      
      <md:surname>Selesnick</md:surname>
      <md:email>selesi@taco.poly.edu</md:email>
    </md:author>
  </md:authorlist>

  <md:maintainerlist>
    <md:maintainer id="selesi">
      <md:firstname>Ivan</md:firstname>
      
      <md:surname>Selesnick</md:surname>
      <md:email>selesi@taco.poly.edu</md:email>
    </md:maintainer>
    <md:maintainer id="charlet">
      <md:firstname>Charlet</md:firstname>
      
      <md:surname>Reedstrom</md:surname>
      <md:email>charlet@rice.edu</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  <md:keywordlist>
    <md:keyword>LTI</md:keyword>
    <md:keyword>Discrete-Time</md:keyword>
    <md:keyword>Continuous-Time</md:keyword>
  </md:keywordlist>

  <md:abstract/>
</metadata>

  <content>
    <section id="secdt">
      <name>Discrete-Time</name>
      <exercise id="ex1">
	<problem>
	  <para id="dt1">
	    The diagrams show the impulse responses (<cnxn target="irfig1"/>), frequency responses (<cnxn target="frfig1"/>) and pole-zero diagrams (<cnxn target="zpfig1"/>) of 4 causal discrete-time LTI
	      systems.  But the diagrams are out of order.  Match each
	      diagram by filling out <cnxn target="table1"/>.

	    <table id="table1" frame="all">
	      <tgroup cols="3" colsep="1" rowsep="1">
		<thead>
		  <row>
		    <entry align="center">Impulse Response</entry>
		    <entry align="center">Frequency Response</entry>
		    <entry align="center">Pole-Zero Diagram</entry>
		  </row>
		</thead>
		<tbody>
		  <row>
		    <entry align="center">1</entry>
		    <entry align="center"/>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">2</entry>
		    <entry align="center"/>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">3</entry>
		    <entry align="center"/>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">4</entry>
		    <entry align="center"/>
		    <entry align="center"/>
		  </row>
		</tbody>
	      </tgroup>
	    </table>

	    <figure id="irfig1">
	      <media type="application/postscript" src="DTMatching_MatchA_ImpulseResp.eps">
		<media type="image/png" src="DTMatching_MatchA_ImpulseResp.png"/>
	      </media>
	      <caption/>
	    </figure>

	    <figure id="frfig1">
	      <media type="application/postscript" src="DTMatching_MatchA_FreqResp.eps">
		<media type="image/png" src="DTMatching_MatchA_FreqResp.png"/>
	      </media>
	      <caption/>
	    </figure>

	    <figure id="zpfig1">
	      <media type="application/postscript" src="DTMatching_MatchA_PoleZero.eps">
		<media type="image/png" src="DTMatching_MatchA_PoleZero.png"/>
	      </media>
	      <caption>
		In these pole-zero diagrams, the zeros are shown with
		"o" and the poles are shown by "x".
	      </caption>
	    </figure>
	  </para>
	</problem>

<!--	<solution>
	  <table id='table1s' frame='all'>
	    <tgroup cols='3' colsep="1" rowsep="1">
	      <thead>
		<row>
		  <entry align="center">Impulse Response</entry>
		  <entry align="center">Frequency Response</entry>
		  <entry align="center">Pole-Zero Diagram</entry>
		</row>
	      </thead>
	      <tbody>
		<row>
		  <entry align="center">1</entry>
		  <entry align="center"></entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">2</entry>
		  <entry align="center"></entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">3</entry>
		  <entry align="center"></entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">4</entry>
		  <entry align="center"></entry>
		  <entry align="center"></entry>
		</row>
	      </tbody>
	    </tgroup>
	  </table>
	</solution>-->
      </exercise>

      <exercise id="ex2">
	<problem>
	  <para id="dt2">
	    The diagrams show the impulse responses (<cnxn target="irfig2"/>), frequency responses (<cnxn target="frfig2"/>) and pole-zero diagrams (<cnxn target="zpfig2"/>) of 4 causal discrete-time LTI
	      systems.  But the diagrams are out of order.  Match each
	      diagram by filling out <cnxn target="table2"/>.

	    <table id="table2" frame="all">
	      <tgroup cols="3" colsep="1" rowsep="1">
		<thead>
		  <row>
		    <entry align="center">Impulse Response</entry>
		    <entry align="center">Frequency Response</entry>
		    <entry align="center">Pole-Zero Diagram</entry>
		  </row>
		</thead>
		<tbody>
		  <row>
		    <entry align="center">1</entry>
		    <entry align="center"/>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">2</entry>
		    <entry align="center"/>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">3</entry>
		    <entry align="center"/>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">4</entry>
		    <entry align="center"/>
		    <entry align="center"/>
		  </row>
		</tbody>
	      </tgroup>
	    </table>

	    <figure id="irfig2">
	      <media type="application/postscript" src="DTMatching_MatchB_ImpulseResp.eps">
		<media type="image/png" src="DTMatching_MatchB_ImpulseResp.png"/>
	      </media>
	      <caption/>
	    </figure>

	    <figure id="frfig2">
	      <media type="application/postscript" src="DTMatching_MatchB_FreqResp.eps">
		<media type="image/png" src="DTMatching_MatchB_FreqResp.png"/>
	      </media>
	      <caption/>
	    </figure>

	    <figure id="zpfig2">
	      <media type="application/postscript" src="DTMatching_MatchB_PoleZero.eps">
		<media type="image/png" src="DTMatching_MatchB_PoleZero.png"/>
	      </media>
	      <caption>
		In these pole-zero diagrams, the zeros are shown with
		"o" and the poles are shown by "x".
	      </caption>
	    </figure>
	  </para>
	</problem>

<!--	<solution>
	  <table id='table2s' frame='all'>
	    <tgroup cols='3' colsep="1" rowsep="1">
	      <thead>
		<row>
		  <entry align="center">Impulse Response</entry>
		  <entry align="center">Frequency Response</entry>
		  <entry align="center">Pole-Zero Diagram</entry>
		</row>
	      </thead>
	      <tbody>
		<row>
		  <entry align="center">1</entry>
		  <entry align="center"></entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">2</entry>
		  <entry align="center"></entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">3</entry>
		  <entry align="center"></entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">4</entry>
		  <entry align="center"></entry>
		  <entry align="center"></entry>
		</row>
	      </tbody>
	    </tgroup>
	  </table>
	</solution>-->
      </exercise>

      <exercise id="ex3">
	<problem>
	  <para id="dt3">
	    The diagrams show the impulse responses (<cnxn target="irfig3"/>) and pole-zero diagrams (<cnxn target="zpfig3"/>) of 8 causal discrete-time LTI
	      systems.  But the diagrams are out of order.  Match each
	      diagram by filling out <cnxn target="table3"/>.

	    <table id="table3" frame="all">
	      <tgroup cols="2" colsep="1" rowsep="1">
		<thead>
		  <row>
		    <entry align="center">Impulse Response</entry>
		    <entry align="center">Pole-Zero Diagram</entry>
		  </row>
		</thead>
		<tbody>
		  <row>
		    <entry align="center">1</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">2</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">3</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">4</entry>
		    <entry align="center"/>
		  </row>
		<row>
		  <entry align="center">5</entry>
		  <entry align="center"/>
		</row>
		<row>
		  <entry align="center">6</entry>
		  <entry align="center"/>
		</row>
		<row>
		  <entry align="center">7</entry>
		  <entry align="center"/>
		</row>
		<row>
		  <entry align="center">8</entry>
		  <entry align="center"/>
		</row>
		</tbody>
	      </tgroup>
	    </table>

	    <figure id="irfig3">
	      <media type="application/postscript" src="DTMatching_SecondOrderMatching_Match1_h.eps">
		<media type="image/png" src="DTMatching_SecondOrderMatching_Match1_h.png"/>
	      </media>
	      <caption/>
	    </figure>

	    <figure id="zpfig3">
	      <media type="application/postscript" src="DTMatching_SecondOrderMatching_Match1_pz.eps">
		<media type="image/png" src="DTMatching_SecondOrderMatching_Match1_pz.png"/>
	      </media>
	      <caption>
		In these pole-zero diagrams, the zeros are shown with
		"o" and the poles are shown by "x".
	      </caption>
	    </figure>
	  </para>
	</problem>

<!--	<solution>
	  <table id='table3s' frame='all'>
	    <tgroup cols='2' colsep="1" rowsep="1">
	      <thead>
		<row>
		  <entry align="center">Impulse Response</entry>
		  <entry align="center">Pole-Zero Diagram</entry>
		</row>
	      </thead>
	      <tbody>
		<row>
		  <entry align="center">1</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">2</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">3</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">4</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">5</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">6</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">7</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">8</entry>
		  <entry align="center"></entry>
		</row>
	      </tbody>
	    </tgroup>
	  </table>
	</solution>-->
      </exercise>

      <exercise id="ex4">
	<problem>
	  <para id="dt4">
	    The diagrams show the frequency responses magnitudes 
	    <m:math>
	      <m:apply>
		<m:abs/>
		<m:apply>
		  <m:power/>
		  <m:apply>
		    <m:ci type="fn">H</m:ci>
		    <m:ci>ω</m:ci>
		  </m:apply>
		  <m:ci>f</m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>
	    (<cnxn target="frfig4"/>) and pole-zero diagrams (<cnxn target="zpfig4"/>) of 8 causal discrete-time LTI
 	      systems.  But the diagrams are out of order.  Match each
 	      diagram by filling out <cnxn target="table4"/>.

	    <table id="table4" frame="all">
	      <tgroup cols="2" colsep="1" rowsep="1">
		<thead>
		  <row>
		    <entry align="center">Frequency Response</entry>
		    <entry align="center">Pole-Zero Diagram</entry>
		  </row>
		</thead>
		<tbody>
		  <row>
		    <entry align="center">1</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">2</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">3</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">4</entry>
		    <entry align="center"/>
		  </row>
		<row>
		  <entry align="center">5</entry>
		  <entry align="center"/>
		</row>
		<row>
		  <entry align="center">6</entry>
		  <entry align="center"/>
		</row>
		<row>
		  <entry align="center">7</entry>
		  <entry align="center"/>
		</row>
		<row>
		  <entry align="center">8</entry>
		  <entry align="center"/>
		</row>
		</tbody>
	      </tgroup>
	    </table>

	    <figure id="frfig4">
	      <media type="application/postscript" src="DTMatching_SecondOrderMatching_Match2_H.eps">
		<media type="image/png" src="DTMatching_SecondOrderMatching_Match2_H.png"/>
	      </media>
	      <caption/>
	    </figure>

	    <figure id="zpfig4">
	      <media type="application/postscript" src="DTMatching_SecondOrderMatching_Match2_pz.eps">
		<media type="image/png" src="DTMatching_SecondOrderMatching_Match2_pz.png"/>
	      </media>
	      <caption>
		In these pole-zero diagrams, the zeros are shown with
		"o" and the poles are shown by "x".
	      </caption>
	    </figure>
	  </para>
	</problem>

<!--	<solution>
	  <table id='table4s' frame='all'>
	    <tgroup cols='2' colsep="1" rowsep="1">
	      <thead>
		<row>
		  <entry align="center">Frequency Response</entry>
		  <entry align="center">Pole-Zero Diagram</entry>
		</row>
	      </thead>
	      <tbody>
		<row>
		  <entry align="center">1</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">2</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">3</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">4</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">5</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">6</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">7</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">8</entry>
		  <entry align="center"></entry>
		</row>
	      </tbody>
	    </tgroup>
	  </table>
	</solution>-->
      </exercise>

      <exercise id="ex6">
	<problem>
	  <para id="dt6">
	    The diagrams show the frequency responses (<cnxn target="frfig6"/>), impulse responses (<cnxn target="irfig6"/>), and pole-zero diagrams (<cnxn target="zpfig6"/>) of 4 causal discrete-time LTI
	      systems.  But the diagrams are out of order.  Match each
	      diagram by filling out <cnxn target="table6"/>.

	    <table id="table6" frame="all">
	      <tgroup cols="3" colsep="1" rowsep="1">
		<thead>
		  <row>
		    <entry align="center">Frequency Response</entry>
		    <entry align="center">Pole-Zero Diagram</entry>
		    <entry align="center">Impulse Response</entry>
		  </row>
		</thead>
		<tbody>
		  <row>
		    <entry align="center">1</entry>
		    <entry align="center"/>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">2</entry>
		    <entry align="center"/>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">3</entry>
		    <entry align="center"/>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">4</entry>
		    <entry align="center"/>
		    <entry align="center"/>
		  </row>
		</tbody>
	      </tgroup>
	    </table>

	    <figure id="frfig6">
	      <media type="application/postscript" src="DTMatching_MatchC_FreqResp.eps">
		<media type="image/png" src="DTMatching_MatchC_FreqResp.png"/>
	      </media>
	      <caption/>
	    </figure>

	    <figure id="irfig6">
	      <media type="application/postscript" src="DTMatching_MatchC_ImpulseResp.eps">
		<media type="image/png" src="DTMatching_MatchC_ImpulseResp.png"/>
	      </media>
	      <caption/>
	    </figure>

	    <figure id="zpfig6">
	      <media type="application/postscript" src="DTMatching_MatchC_PoleZero.eps">
		<media type="image/png" src="DTMatching_MatchC_PoleZero.png"/>
	      </media>
	      <caption>
		In these pole-zero diagrams, the zeros are shown with
		"o" and the poles are shown by "x".
	      </caption>
	    </figure>
	  </para>
	</problem>

<!--	<solution>
	  <table id='table6s' frame='all'>
	    <tgroup cols='3' colsep="1" rowsep="1">
	      <thead>
		<row>
		  <entry align="center">Frequency Response</entry>
		  <entry align="center">Pole-Zero Diagram</entry>
		  <entry align="center">Impulse Response</entry>
		</row>
	      </thead>
	      <tbody>
		<row>
		  <entry align="center">1</entry>
		  <entry align="center"></entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">2</entry>
		  <entry align="center"></entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">3</entry>
		  <entry align="center"></entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">4</entry>
		  <entry align="center"></entry>
		  <entry align="center"></entry>
		</row>
	      </tbody>
	    </tgroup>
	  </table>
	</solution>-->
      </exercise>

      <exercise id="ex7">
	<problem>
	  <para id="dt7">
	    The diagrams show the frequency responses (<cnxn target="frfig7"/>) and pole-zero diagrams (<cnxn target="zpfig7"/>) of 6 causal discrete-time LTI
	      systems.  But the diagrams are out of order.  Match each
	      diagram by filling out <cnxn target="table7"/>.

	    <table id="table7" frame="all">
	      <tgroup cols="2" colsep="1" rowsep="1">
		<thead>
		  <row>
		    <entry align="center">Frequency Response</entry>
		    <entry align="center">Pole-Zero Diagram</entry>
		  </row>
		</thead>
		<tbody>
		  <row>
		    <entry align="center">1</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">2</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">3</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">4</entry>
		    <entry align="center"/>
		  </row>
		<row>
		  <entry align="center">5</entry>
		  <entry align="center"/>
		</row>
		<row>
		  <entry align="center">6</entry>
		  <entry align="center"/>
		</row>
		</tbody>
	      </tgroup>
	    </table>

	    <figure id="frfig7">
	      <media type="application/postscript" src="DTMatching_MatchD_FreqResp.eps">
		<media type="image/png" src="DTMatching_MatchD_FreqResp.png"/>
	      </media>
	      <caption/>
	    </figure>

	    <figure id="zpfig7">
	      <media type="application/postscript" src="DTMatching_MatchD_PoleZero.eps">
		<media type="image/png" src="DTMatching_MatchD_PoleZero.png"/>
	      </media>
	      <caption>
		In these pole-zero diagrams, the zeros are shown with
		"o" and the poles are shown by "x".
	      </caption>
	    </figure>
	  </para>
	</problem>

<!--	<solution>
	  <table id='table7s' frame='all'>
	    <tgroup cols='2' colsep="1" rowsep="1">
	      <thead>
		<row>
		  <entry align="center">Frequency Response</entry>
		  <entry align="center">Pole-Zero Diagram</entry>
		</row>
	      </thead>
	      <tbody>
		<row>
		  <entry align="center">1</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">2</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">3</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">4</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">5</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">6</entry>
		  <entry align="center"></entry>
		</row>
	      </tbody>
	    </tgroup>
	  </table>
	</solution>-->
      </exercise>


      <exercise id="ex8">
	<problem>
	  <para id="dt8">
	    The diagrams show the pole-zero diagrams (<cnxn target="zpfig8"/>) and impulse responses (<cnxn target="irfig8"/>) of 8 causal discrete-time LTI
	      systems.  But the diagrams are out of order.  Match each
	      diagram by filling out <cnxn target="table8"/>.

	    <table id="table8" frame="all">
	      <tgroup cols="2" colsep="1" rowsep="1">
		<thead>
		  <row>
		    <entry align="center">Pole-Zero Diagram</entry>
		    <entry align="center">Impulse Response</entry>
		  </row>
		</thead>
		<tbody>
		  <row>
		    <entry align="center">1</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">2</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">3</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">4</entry>
		    <entry align="center"/>
		  </row>
		<row>
		  <entry align="center">5</entry>
		  <entry align="center"/>
		</row>
		<row>
		  <entry align="center">6</entry>
		  <entry align="center"/>
		</row>
		<row>
		  <entry align="center">7</entry>
		  <entry align="center"/>
		</row>
		<row>
		  <entry align="center">8</entry>
		  <entry align="center"/>
		</row>
		</tbody>
	      </tgroup>
	    </table>

	    <figure id="zpfig8">
	      <media type="application/postscript" src="DTMatching_PoleZero_PoleZero.eps">
		<media type="image/png" src="DTMatching_PoleZero_PoleZero.png"/>
	      </media>
	      <caption>
		In these pole-zero diagrams, the zeros are shown with
		"o" and the poles are shown by "x".
	      </caption>
	    </figure>

	    <figure id="irfig8">
	      <media type="application/postscript" src="DTMatching_PoleZero_ImpulseResponse.eps">
		<media type="image/png" src="DTMatching_PoleZero_ImpulseResponse.png"/>
	      </media>
	      <caption/>
	    </figure>
	  </para>
	</problem>

<!--	<solution>
	  <table id='table8s' frame='all'>
	    <tgroup cols='2' colsep="1" rowsep="1">
	      <thead>
		<row>
		  <entry align="center">Impulse Response</entry>
		  <entry align="center">Pole-Zero Diagram</entry>
		</row>
	      </thead>
	      <tbody>
		<row>
		  <entry align="center">1</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">2</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">3</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">4</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">5</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">6</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">7</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">8</entry>
		  <entry align="center"></entry>
		</row>
	      </tbody>
	    </tgroup>
	  </table>
	</solution>-->
      </exercise>
    </section>

    <section id="ct">
      <name>Continuous-Time</name>

      <exercise id="exct1">
	<problem>
	  <para id="ct1">
	    Match the impulse response 
	    <m:math>
	      <m:apply>
		<m:ci type="fn">h</m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math> of a continuous-time LTI system with the correct
	    plot of its frequency response
	    <m:math>
	      <m:apply>
		<m:abs/>
		<m:apply>
		  <m:power/>
		  <m:apply>
		    <m:ci type="fn">H</m:ci>
		    <m:ci>ω</m:ci>
		  </m:apply>
		  <m:ci>f</m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>.  <emphasis>Explain how you obtain your
	    answer.</emphasis>
     

	    <figure id="irfigct1">
	      <media type="application/postscript" src="CTMatching_Match_FR_IR_hH1.eps">
		<media type="image/png" src="CTMatching_Match_FR_IR_hH1.png"/>
	      </media>
	      <caption/>
	    </figure>

	    <figure id="frfigct1">
	      <media type="application/postscript" src="CTMatching_Match_FR_IR_hH2.eps">
		<media type="image/png" src="CTMatching_Match_FR_IR_hH2.png"/>
	      </media>
	      <caption/>
	    </figure>
	  </para>
	</problem>
<!--	<solution>
	  <para id='ct1s'>
	    No answer available at this time.
	  </para>
	</solution>-->
      </exercise>

      <exercise id="exct2">
	<problem>
	  <para id="ct2">
	    For the impulse response 
	    <m:math>
	      <m:apply>
		<m:ci type="fn">h</m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math> illustrated in <cnxn target="irfigct1"/>,
	    identify the correct diagram of the poles of
	    <m:math>
	      <m:apply>
		<m:ci type="fn">H</m:ci>
		<m:ci>s</m:ci>
	      </m:apply>
	    </m:math>.  <emphasis>Explain how you obtain your
	    answer.</emphasis>

	    <figure id="polesfigct2">
	      <media type="application/postscript" src="CTMatching_Match_FR_IR_HP.eps">
		<media type="image/png" src="CTMatching_Match_FR_IR_HP.png"/>
	      </media>
	      <caption/>
	    </figure>
	  </para>
	</problem>
<!--	<solution>
	  <para id='ct2s'>
	  </para>
	</solution>-->
      </exercise>

      <exercise id="exct3">
	<problem>
	  <para id="ct3">
	    <cnxn target="polesfigct3"/> indicate the pole locations
	    of six continuous-time LTI systems.  Match each with the
	    corresponding impulse response (<cnxn target="irfigct3"/>)
	    without actually computing the Laplace transform.

	    <table id="tablect3" frame="all">
	      <tgroup cols="2" colsep="1" rowsep="1">
		<thead>
		  <row>
		    <entry align="center">Pole-Zero Diagram</entry>
		    <entry align="center">Impulse Response</entry>
		  </row>
		</thead>
		<tbody>
		  <row>
		    <entry align="center">1</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">2</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">3</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">4</entry>
		    <entry align="center"/>
		  </row>
		<row>
		  <entry align="center">5</entry>
		  <entry align="center"/>
		</row>
		<row>
		  <entry align="center">6</entry>
		  <entry align="center"/>
		</row>
		</tbody>
	      </tgroup>
	    </table>

	    <figure id="polesfigct3">
	      <media type="application/postscript" src="CTMatching_MATLAB4_FIGPD.eps">
		<media type="image/png" src="CTMatching_MATLAB4_FIGPD.png"/>
	      </media>
	      <caption/>
	    </figure>

	    <figure id="irfigct3">
	      <media type="application/postscript" src="CTMatching_MATLAB4_FIGIM.eps">
		<media type="image/png" src="CTMatching_MATLAB4_FIGIM.png"/>
	      </media>
	      <caption/>
	    </figure>
	  </para>
	</problem>

<!--	<solution>
	  <table id='tablect3s' frame='all'>
	    <tgroup cols='2' colsep="1" rowsep="1">
	      <thead>
		<row>
		  <entry align="center">Pole-Zero Diagram</entry>
		  <entry align="center">Impulse Response</entry>
		</row>
	      </thead>
	      <tbody>
		<row>
		  <entry align="center">1</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">2</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">3</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">4</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">5</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">6</entry>
		  <entry align="center"></entry>
		</row>
	      </tbody>
	    </tgroup>
	  </table>
	</solution>-->
      </exercise>

      <exercise id="exct4">
	<problem>
	  <para id="ct4">
	    <cnxn target="frirfigct4"/> shows the impulse responses
	    and frequency responses of four continuous-time LTI
	    systems.  But they are out of order.  Match the impulse
	    response to its frequency response magnitude, and
	    <emphasis>explain</emphasis> your answer.

	    <table id="tablect4" frame="all">
	      <tgroup cols="2" colsep="1" rowsep="1">
		<thead>
		  <row>
		    <entry align="center">Impulse Response</entry>
		    <entry align="center">Frequency Response</entry>
		  </row>
		</thead>
		<tbody>
		  <row>
		    <entry align="center">1</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">2</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">3</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">4</entry>
		    <entry align="center"/>
		  </row>
		</tbody>
	      </tgroup>
	    </table>

	    <figure id="frirfigct4">
	      <media type="application/postscript" src="CTMatching_MATLAB2_FIG.eps">
		<media type="image/png" src="CTMatching_MATLAB2_FIG.png"/>
	      </media>
	      <caption/>
	    </figure>
	  </para>
	</problem>

<!--	<solution>
	  <table id='tablect4s' frame='all'>
	    <tgroup cols='2' colsep="1" rowsep="1">
	      <thead>
		<row>
		  <entry align="center">Impulse Response</entry>
		  <entry align="center">Frequency Response</entry>
		</row>
	      </thead>
	      <tbody>
		<row>
		  <entry align="center">1</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">2</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">3</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">4</entry>
		  <entry align="center"></entry>
		</row>
	      </tbody>
	    </tgroup>
	  </table>
	</solution>-->
      </exercise>

      <exercise id="exct5">
	<problem>
	  <para id="ct5">
	    <cnxn target="frirfigct5"/> shows the impulse responses and
	    frequency responses of four continuous-time LTI systems.
	    But they are out of order.  Match each impulse response with
	    its frequency response.

	    <table id="tablect5" frame="all">
	      <tgroup cols="2" colsep="1" rowsep="1">
		<thead>
		  <row>
		    <entry align="center">Impulse Response</entry>
		    <entry align="center">Frequency Response</entry>
		  </row>
		</thead>
		<tbody>
		  <row>
		    <entry align="center">1</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">2</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">3</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">4</entry>
		    <entry align="center"/>
		  </row>
		</tbody>
	      </tgroup>
	    </table>

	    <figure id="frirfigct5">
	      <media type="application/postscript" src="CTMatching_Hh2_FREQFIG.eps">
		<media type="image/png" src="CTMatching_Hh2_FREQFIG.png"/>
	      </media>
	      <caption/>
	    </figure>
	  </para>
	</problem>

<!--	<solution>
	  <table id='tablect5s' frame='all'>
	    <tgroup cols='2' colsep="1" rowsep="1">
	      <thead>
		<row>
		  <entry align="center">Impulse Response</entry>
		  <entry align="center">Frequency Response</entry>
		</row>
	      </thead>
	      <tbody>
		<row>
		  <entry align="center">1</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">2</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">3</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">4</entry>
		  <entry align="center"></entry>
		</row>
	      </tbody>
	    </tgroup>
	  </table>
	</solution>-->
      </exercise>

      <exercise id="exct6">
	<problem>
	  <para id="ct6">
	    <cnxn target="poleirfigct6"/> shows the pole diagrams and
	    frequency responses of four continuous-time LTI systems.
	    But they are out of order.  Match each pole diagram with
	    its frequency response.

	    <table id="tablect6" frame="all">
	      <tgroup cols="2" colsep="1" rowsep="1">
		<thead>
		  <row>
		    <entry align="center">Pole Diagram</entry>
		    <entry align="center">Frequency Response</entry>
		  </row>
		</thead>
		<tbody>
		  <row>
		    <entry align="center">1</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">2</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">3</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">4</entry>
		    <entry align="center"/>
		  </row>
		</tbody>
	      </tgroup>
	    </table>

	    <figure id="poleirfigct6">
	      <media type="application/postscript" src="CTMatching_zpH_FREQFIG.eps">
		<media type="image/png" src="CTMatching_zpH_FREQFIG.png"/>
	      </media>
	      <caption/>
	    </figure>
	  </para>
	</problem>

<!--	<solution>
	  <table id='tablect6s' frame='all'>
	    <tgroup cols='2' colsep="1" rowsep="1">
	      <thead>
		<row>
		  <entry align="center">Pole Diagram</entry>
		  <entry align="center">Frequency Response</entry>
		</row>
	      </thead>
	      <tbody>
		<row>
		  <entry align="center">1</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">2</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">3</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">4</entry>
		  <entry align="center"></entry>
		</row>
	      </tbody>
	    </tgroup>
	  </table>
	</solution>-->
      </exercise>

      <exercise id="exct7">
	<problem>
	  <para id="ct7">
	    The diagrams show the pole-zero diagrams (<cnxn target="zpfigct7"/>) and frequency responses (<cnxn target="frfigct7"/>) of 8 causal discrete-time LTI
	      systems.  But the diagrams are out of order.  Match each
	      diagram by filling out <cnxn target="tablect7"/>.

	    <table id="tablect7" frame="all">
	      <tgroup cols="2" colsep="1" rowsep="1">
		<thead>
		  <row>
		    <entry align="center">Pole-Zero Diagram</entry>
		    <entry align="center">Frequency Response</entry>
		  </row>
		</thead>
		<tbody>
		  <row>
		    <entry align="center">1</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">2</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">3</entry>
		    <entry align="center"/>
		  </row>
		  <row>
		    <entry align="center">4</entry>
		    <entry align="center"/>
		  </row>
		<row>
		  <entry align="center">5</entry>
		  <entry align="center"/>
		</row>
		<row>
		  <entry align="center">6</entry>
		  <entry align="center"/>
		</row>
		<row>
		  <entry align="center">7</entry>
		  <entry align="center"/>
		</row>
		<row>
		  <entry align="center">8</entry>
		  <entry align="center"/>
		</row>
		</tbody>
	      </tgroup>
	    </table>

	    <figure id="zpfigct7">
	      <media type="application/postscript" src="CTMatching_MatchPZ_PoleZero.eps">
		<media type="image/png" src="CTMatching_MatchPZ_PoleZero.png"/>
	      </media>
	      <caption>
		In these pole-zero diagrams, the zeros are shown with
		"o" and the poles are shown by "x".
	      </caption>
	    </figure>

	    <figure id="frfigct7">
	      <media type="application/postscript" src="CTMatching_MatchPZ_FreqResponse.eps">
		<media type="image/png" src="CTMatching_MatchPZ_FreqResponse.png"/>
	      </media>
	      <caption/>
	    </figure>
	  </para>
	</problem>

<!--	<solution>
	  <table id='tablect7s' frame='all'>
	    <tgroup cols='2' colsep="1" rowsep="1">
	      <thead>
		<row>
		  <entry align="center">Pole-Zero Diagram</entry>
		  <entry align="center">Frequency Response</entry>
		</row>
	      </thead>
	      <tbody>
		<row>
		  <entry align="center">1</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">2</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">3</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">4</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">5</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">6</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">7</entry>
		  <entry align="center"></entry>
		</row>
		<row>
		  <entry align="center">8</entry>
		  <entry align="center"></entry>
		</row>
	      </tbody>
	    </tgroup>
	  </table>
	</solution>-->
      </exercise>

      <exercise id="exct9">
	<problem>
	  <para id="ct9">
	    The figures show two input signals 
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>x</m:mi>
		    <m:mn>1</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math> and 
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>x</m:mi>
		    <m:mn>2</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>, two impulse responses 
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>h</m:mi>
		    <m:mn>1</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math> and 
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>h</m:mi>
		    <m:mn>2</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math> (see <cnxn target="figct9a"/>), and four output signals 
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>y</m:mi>
		    <m:mn>1</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>,
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>y</m:mi>
		    <m:mn>2</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>,
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>y</m:mi>
		    <m:mn>3</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>,
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>y</m:mi>
		    <m:mn>4</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math> (see <cnxn target="figct9b"/>).  Identify which
	    input signal and which impulse response causes each of the
	    four output signals.  (Your answer should have four parts;
	    <m:math>
	      <m:apply>
		<m:eq/>
		<m:apply>
		  <m:ci type="fn"><m:msub>
		      <m:mi>y</m:mi>
		      <m:mn>1</m:mn>
		    </m:msub></m:ci>
		  <m:ci>t</m:ci>
		</m:apply>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#convolve"/>
		  <m:apply>
		    <m:ci type="fn"><m:msub>
			<m:mi>h</m:mi>
			<m:mi>?</m:mi>
		      </m:msub></m:ci>
		    <m:ci>t</m:ci>
		  </m:apply>
		  <m:apply>
		    <m:ci type="fn"><m:msub>
			<m:mi>x</m:mi>
			<m:mi>?</m:mi>
		      </m:msub></m:ci>
		    <m:ci>t</m:ci>
		  </m:apply>
		</m:apply>
	      </m:apply>
	    </m:math>, <foreign>etc.</foreign>)

	    <figure id="figct9a">
	      <media type="application/postscript" src="CTMatching_MATLAB_FIG1.eps">
		<media type="image/png" src="CTMatching_MATLAB_FIG1.png"/>
	      </media>
	      <caption/>
	    </figure>

	    <figure id="figct9b">
	      <media type="application/postscript" src="CTMatching_MATLAB_FIG2.eps">
		<media type="image/png" src="CTMatching_MATLAB_FIG2.png"/>
	      </media>
	      <caption/>
	    </figure>
	  </para>
	</problem>
<!--	<solution>
	  <para id='ct9s'>
	  </para>
	</solution>-->
      </exercise>

      <exercise id="exct10">
	<problem>
	  <para id="ct10">
	    The figures show two input signals 
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>x</m:mi>
		    <m:mn>1</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math> and 
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>x</m:mi>
		    <m:mn>2</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>, two impulse responses 
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>h</m:mi>
		    <m:mn>1</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math> (see <cnxn target="figct10a"/>) and 
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>h</m:mi>
		    <m:mn>2</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>, and four output signals 
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>y</m:mi>
		    <m:mn>1</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>,
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>y</m:mi>
		    <m:mn>2</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>,
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>y</m:mi>
		    <m:mn>3</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>,
	    <m:math>
	      <m:apply>
		<m:ci type="fn"><m:msub>
		    <m:mi>y</m:mi>
		    <m:mn>4</m:mn>
		  </m:msub></m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math> (see <cnxn target="figct10b"/>).  Identify which
	    input signal and which impulse response causes each of the
	    four output signals.  (Your answer should have four parts;
	    <m:math>
	      <m:apply>
		<m:eq/>
		<m:apply>
		  <m:ci type="fn"><m:msub>
		      <m:mi>y</m:mi>
		      <m:mn>1</m:mn>
		    </m:msub></m:ci>
		  <m:ci>t</m:ci>
		</m:apply>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#convolve"/>
		  <m:apply>
		    <m:ci type="fn"><m:msub>
			<m:mi>h</m:mi>
			<m:mi>?</m:mi>
		      </m:msub></m:ci>
		    <m:ci>t</m:ci>
		  </m:apply>
		  <m:apply>
		    <m:ci type="fn"><m:msub>
			<m:mi>x</m:mi>
			<m:mi>?</m:mi>
		      </m:msub></m:ci>
		    <m:ci>t</m:ci>
		  </m:apply>
		</m:apply>
	      </m:apply>
	    </m:math>, <foreign>etc.</foreign>)

	    <figure id="figct10a">
	      <media type="application/postscript" src="CTMatching_MATLAB3_FIG1.eps">
		<media type="image/png" src="CTMatching_MATLAB3_FIG1.png"/>
	      </media>
	      <caption/>
	    </figure>

	    <figure id="figct10b">
	      <media type="application/postscript" src="CTMatching_MATLAB3_FIG2.eps">
		<media type="image/png" src="CTMatching_MATLAB3_FIG2.png"/>
	      </media>
	      <caption/>
	    </figure>
	  </para>
	</problem>
<!--	<solution>
	  <para id='ct10s'>
	  </para>
	</solution>-->
      </exercise>

    </section>
  </content>
  
</document>
