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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/">Baseband Communication</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/">
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      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Don</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Johnson</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">dhj@rice.edu</md:email>
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      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Don</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Johnson</md:surname>
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      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Joe</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Montgomery</md:surname>
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      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Erin</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Snavely</md:surname>
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    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">analog communication</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">analog signal</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">baseband communication</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">baseband signal</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">information communication</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">signal-to-noise ratio</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">SNR</md:keyword>
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  <md:abstract xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Baseband communication is the simplest form of analog communication.</md:abstract>
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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="p1">
      We use analog communication techniques for analog message
      signals, like music, speech, and television.  Transmission and
      reception of analog signals using analog results in an
      inherently noisy received signal (assuming the channel adds
      noise, which it almost certainly does).</para>
    

    <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="p2">
      The simplest form of analog communication is <term xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">baseband
      communication</term>.
      
      <note 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="Point of Interest">We use analog communication
	techniques for analog message signals, like music, speech, and
	television. Transmission and reception of analog signals using
	analog results in an inherently noisy received signal
	(assuming the channel adds noise, which it almost certainly
	does).</note>

      Here, the transmitted signal equals the message times a
      transmitter gain.
      
      <equation 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="eqn0000">
	<m:math>
	  <m:apply>
	    <m:eq/>
	    <m:apply>
	      <m:ci type="fn">x</m:ci><m:ci>t</m:ci>
	    </m:apply>
	    <m:apply>
	      <m:times/>
	      <m:ci>G</m:ci>
	      <m:apply>
		<m:ci type="fn">m</m:ci><m:ci>t</m:ci>
	      </m:apply>
	    </m:apply>
	  </m:apply>
	</m:math>
	
      </equation>
      An example, which is somewhat out of date, is the wireline
      telephone system. You don't use baseband communication in
      wireless systems simply because low-frequency signals do not
      radiate well. The receiver in a baseband system can't do much
      more than filter the received signal to remove out-of-band noise
      (interference is small in wireline channels). Assuming the
      signal occupies a bandwidth of <m:math><m:ci>W</m:ci></m:math>
      Hz (the signal's spectrum extends from zero to
      <m:math><m:ci>W</m:ci></m:math>), the receiver applies a lowpass
      filter having the same bandwidth, as shown in <cnxn xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" target="fig1000" strength="8"/>.
    </para>
    
    <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="fig1000" orient="horizontal">
      <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="sys17.png"/>
      <caption xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">The receiver for baseband communication systems is quite
	simple: a lowpass filter having the same bandwidth as the
	signal. </caption>
    </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="p3">
      We use the <term xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">signal-to-noise ratio </term>of the
      receiver's output 
      <m:math>
	<m:apply>
	  <m:ci type="fn">
	    <m:mover><m:mi>m</m:mi>
	      <m:mo>^</m:mo>
	    </m:mover>
	  </m:ci>
	  <m:ci>t</m:ci>
	</m:apply>
      </m:math>
      to evaluate any analog-message communication system. Assume that
      the channel introduces an attenuation
      <m:math><m:ci>α</m:ci></m:math> and white noise of
      spectral height
      <m:math>
	<m:apply><m:divide/>
	  <m:ci><m:msub><m:mi>N</m:mi><m:mn>0</m:mn></m:msub></m:ci>
	  <m:cn>2</m:cn>
	</m:apply>
      </m:math>.  The filter does not affect the signal component—we
      assume its gain is unity—but does filter the noise,
      removing frequency components above
      <m:math><m:ci>W</m:ci></m:math> Hz.  In the filter's output, the
      received signal power equals
      <m:math>
	<m:apply>
	  <m:times/>
	  <m:apply>
	    <m:power/>
	    <m:ci>α</m:ci>
	    <m:cn>2</m:cn>
	  </m:apply>
	  <m:apply> 
	    <m:power/>
	    <m:ci>G</m:ci>
	    <m:cn>2</m:cn>
	  </m:apply>
	  <m:apply>
	    <m:ci type="fn">power</m:ci><m:ci>m</m:ci>
	  </m:apply>
	</m:apply>
      </m:math>
      and the noise power
      <m:math>
	<m:apply><m:times/>
	  <m:ci><m:msub><m:mi>N</m:mi><m:mn>0</m:mn></m:msub></m:ci>
	  <m:ci>W</m:ci>
	</m:apply>
      </m:math>,
      which gives a signal-to-noise ratio of

      <equation 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="eqn0001">
	<m:math>
	  <m:apply>
	    <m:eq/>
	    <m:ci><m:msub><m:ci>SNR</m:ci><m:mo>baseband</m:mo></m:msub></m:ci>
	    <m:apply>
	      <m:divide/>
	      <m:apply>
		<m:times/>
		<m:apply>
		  <m:power/>
		  <m:ci>α</m:ci>
		  <m:cn>2</m:cn>
		</m:apply>
		<m:apply> 
		  <m:power/>
		  <m:ci>G</m:ci>
		  <m:cn>2</m:cn>
		</m:apply>
		<m:apply>
		  <m:ci type="fn">power</m:ci><m:ci>m</m:ci>
		</m:apply>
	      </m:apply>
	      <m:apply>
		<m:times/>
		<m:ci><m:msub><m:mi>N</m:mi><m:mn>0</m:mn></m:msub></m:ci>
		<m:ci>W</m:ci>
	      </m:apply>
	    </m:apply>
	  </m:apply>
	</m:math>
      </equation>

      The signal power <m:math><m:apply><m:ci type="fn">power</m:ci><m:ci>m</m:ci></m:apply></m:math> will be
      proportional to the bandwidth <m:math><m:ci>W</m:ci></m:math>;
      thus, in baseband communication the signal-to-noise ratio varies
      only with transmitter gain and channel attenuation and noise
      level.
    </para>
  </content>
</document>
