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???
12/21/09 22:36
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#171840 - Undersampling often quite powerful
Responding to: ???'s previous message
When the sampling rate isn't some form of multiple of the frequency you are measuring, you can get the peak by trying enough number of times.

With your suggested frequencies, you will get a loop that will repeat every 500ms, so if starting the sampling when the input signal does a zero-crossing (or in this case a 2.5V crossing) the best value measured would be 3.6 degrees from a maxima, giving 99.8% of the true maxima. This is the worst you will get with these two frequencies. Starting the sampling at another point could get closer to the true maxima.

When undersampling a random signal, you will not be able to recreate the original waveform. But if you do know that the original waveform is a sine wave, then your undersampled signal will also sample a sine wave of the same amplitude (even if no sample may catch a maxima). So if it is known that the input signal is a sine wave, you will be able to compute the amplitude of the 106Hz input signal even if sampling at 100Hz as long as the individual samples are snapshots. So if 99.8% of the true maxima isn't good enough, then a bit of math and the knowledge that the input signal is a sine wave could produce way better results (if the ADC is good enough and reasonably calibrated).

If the sampling frequency had been 99.79Hz instead, the two frequencies would lock in such a tiny sequence, and you would (if starting from zero-crossing) manage 0.3 degrees off after 2.3 seconds, representing 0.999986 of the maxima.

Never underestimate what can be done even when undersampling a signal, as long as the ADC gets snapshots and doesn't do slow iterative conversions against a drifting input signal.

List of 28 messages in thread
TopicAuthorDate
ADuC816 Problem            01/01/70 00:00      
   Sample rate ?            01/01/70 00:00      
   Isn't that exactly what you should get?            01/01/70 00:00      
      Indeed!            01/01/70 00:00      
         Hmm            01/01/70 00:00      
            average of the repetitive peak ?            01/01/70 00:00      
               Better            01/01/70 00:00      
                  Clarification            01/01/70 00:00      
                     Signal Frequency            01/01/70 00:00      
                        magnitude            01/01/70 00:00      
                           Dump a number of samples to check            01/01/70 00:00      
                        it is possible?            01/01/70 00:00      
                           fast sample-and-hold            01/01/70 00:00      
                              sorry, but            01/01/70 00:00      
                                 and            01/01/70 00:00      
                                    it won't            01/01/70 00:00      
                                       Undersampling often quite powerful            01/01/70 00:00      
                                          what is conclusion for OP?            01/01/70 00:00      
                              How about precision rectification?            01/01/70 00:00      
   re:ADUC816            01/01/70 00:00      
      sure, you can            01/01/70 00:00      
      Most cheaper digital scopes uses repetitive sampling            01/01/70 00:00      
      how about            01/01/70 00:00      
         SF=1            01/01/70 00:00      
            Consistent not a simple subset of accurate            01/01/70 00:00      
               Dumping Values            01/01/70 00:00      
                  *EDIT*            01/01/70 00:00      
                     Circuit            01/01/70 00:00      

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