From: pcdhSpamMeSenseless@electrooptical.net   
      
   On 01/12/2014 10:32 PM, haiticare2011@gmail.com wrote:   
   > On Sunday, January 12, 2014 8:22:18 PM UTC-5, Phil Hobbs wrote:   
   >> On 1/12/2014 12:51 PM, hai...@gmail.com wrote:   
   >>   
   >>> Oz: When you control both the emitter (eg led) and sensor (eg PD   
   >>> with   
   >>   
   >> blah blah   
   >>>   
   >>   
   >>> An interesting twist on this lock-in is the algorithm described   
   >>> by   
   >>   
   >>> Horowitz in his Art of Electronics, ca. p. 1027. The algorithm   
   >>> is so   
   >>   
   >>> simple it is mind-bending: Just add many measurements, and the   
   >>   
   >>> "grass" on top of the mountain will become visible. No averaging   
   >>   
   >>> involved in its execution. I know this has been used in the   
   >>> Hubble   
   >>   
   >>> telescope, and wonder if anyone has used this in more mundane   
   >>> apps.   
   >>   
   >>>   
   >>   
   >>> Horowitz explains this by noting that the noise increases as the   
   >>> sqrt   
   >>   
   >>> of number of observations, but the buried signal increases in a   
   >>   
   >>> linear fashion. So, if the measurement value is 100 with noise   
   >>   
   >>> fluctuation 5, and the signal is say .01, then after 10exp6   
   >>   
   >>> measurements, the signal is now 10,000 and the noise fringe   
   >>> 5,000.   
   >>   
   >>>   
   >>   
   >>> The signal value will be 100 million from the addition, so a   
   >>   
   >>> microprocessor seems a good way to do this.   
   >>   
   >>>   
   >>   
   >>   
   >>   
   >>   
   >>   
   >> The only difference between adding and averaging is dividing by   
   >> the   
   >>   
   >> number of measurements.  The SNR improvement is unchanged.  This   
   >> has   
   >>   
   >> been known since the time of Gauss, at least.   
   >>   
   >>   
   >>   
   >> Cheers   
   >>   
   >>   
   >>   
   >> Phil Hobbs   
      
   > hmmm Horowitz (page 1027 AOE) sez: "...the average value contributed   
   > by noise is quite irrelevant: all that matters is the fluctuations   
   > of the average value around the mean." He then goes on to give an   
   > example of Mossbauer spectroscopy which is identical mathematically   
   > to what I was talking about. If you notice the graph (page 1028),   
   > the values are just added to form a noise floor after many samples   
   > are taken. Now, you could just average the final accumulated number   
   > after 100,000 sweeps (in his example), but that would reduce the   
   > effective SNR here, as I see it. In any case, the magic occurs here   
   > in the addition process forming a low "fuzz" noise floor. To say it   
   > is the same as s simple average may confuse, since the "average   
   > averager" may just take enough samples to have his number SD settle   
   > down, whereas there can still be a signal buried in the pile. Just   
   > my reading.   
      
   So what do you think is the difference between averaging and summing?   
      
   IIRC that H&H plot is on a semilog scale, so the division just moves the   
   curve down a bit.   
      
   This is all just math, you don't have to wave a dead chicken over it.   
      
   Cheers   
      
   Phil Hobbs   
      
   --   
   Dr Philip C D Hobbs   
   Principal Consultant   
   ElectroOptical Innovations LLC   
   Optics, Electro-optics, Photonics, Analog Electronics   
      
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