On Friday, January 24, 2014 3:26:37 AM UTC-5, Jeroen Belleman wrote:   
   > On 2014-01-24 05:58, ticare2011@gmail.com wrote:   
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   > [Snipped the mangled text ...   
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   > > Well, I'll skip the first question, as it is complex. But the "signal   
   >    
   > > averaging," as Horowitz describes it, is just an addition, without   
   >    
   > > dividing, of many measurements. His presentation somewhat confusing,   
   >    
   > > as he is separating a Mossbauer resonance signal into frequency   
   >    
   > > bands. But the signal processing action occurs in the cumulative   
   >    
   > > addition. After X additions, the noise variation in the overall   
   >    
   > > signal goes down, and the buried signal shows itself above that   
   >    
   > > noise.   
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   >    
   > Both noise and signal *grow* as more measurements get added.   
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   > It's just that the signal grows faster than the noise, and   
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   > eventually gets to stand out.   
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   > The signal contribution grows linearly with the number of   
   >    
   > sweeps, because it's accumulated coherently, whereas the   
   >    
   > incoherent noise only grows with the square root of the   
   >    
   > number of sweeps. (For a large number of sweeps, of course.)   
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   > The division needed to to properly call this 'averaging' is   
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   > a no-op as regards signal to noise ratio.   
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   >    
   >    
   > Jeroen Belleman   
      
   Hi Jeroen,   
   To be fair, you are correct, the signal IS growing faster than the noise. But   
   what allows Messr. Horowitz to see it is that the 'standard deviation' of the   
   noise goes way down, more than the SD of the signal. So if you do Y   
   measurement episodes of X    
   measures each, the variation in the noise (in the reference beam) will be   
   tight, and the signal (in the measurement beam) will almost always be greater   
   than that tight noise floor.   
      
   To be frank, I am a software person, and to be put algorithms in code, you   
   have to know exactly how the little gears turn.    
      
   JB   
      
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