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).
    
    
      The simplest form of analog communication is baseband
      communication.
      
      
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).
      Here, the transmitted signal equals the message times a
      transmitter gain.
      
      
      An example, which is somewhat out of date, is the wireline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 
WW
      Hz (the signal's spectrum extends from zero to
      
WW), the receiver applies a lowpass
      filter having the same bandwidth, as shown in 
Figure 1.
    
    
    
                                                                     
    
    
      We use the signal-to-noise ratio of the
      receiver's output 
      
	
	    m
	      ^
	    
	  t
      
	  
	    m
	      ^
	    
	  
	  t
	
      to evaluate any analog-message communication system. Assume that
      the channel introduces an attenuation
      αα and white noise of
      spectral height
      
	N02
      
	  N0
	  2
	.  The filter does not affect the signal component—we
      assume its gain is unity—but does filter the noise,
      removing frequency components above
      WW Hz.  In the filter's output, the
      received signal power equals
      
	α2G2powerm
      
	  
	  
	    
	    α
	    2
	  
	   
	    
	    G
	    2
	  
	  
	    powerm
	  
	
      and the noise power
      
	N0W
      
	  N0
	  W
	,
      which gives a signal-to-noise ratio of
      
	
	  SNRbaseband=α2G2powermN0W
	
	    
	    SNRbaseband
	    
	      
	      
		
		
		  
		  α
		  2
		
		 
		  
		  G
		  2
		
		
		  powerm
		
	      
	      
		
		N0
		W
	      
	    
	  
      
(2)
      The signal power 
powermpowerm will be
      proportional to the bandwidth 
WW;
      thus, in baseband communication the signal-to-noise ratio varies
      only with transmitter gain and channel attenuation and noise
      level.
    
  
 
        
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