Wikipedia:Reference desk/Archives/Mathematics/2016 April 17

= April 17 =

Lies, damn lies and Interpolating digitised data
Will a sinc function reconstruction filter always give the best interpretation of the original signal even though the digital version may have been the result of undersampling? ie, what sort of lies can we tell ourselves if we are not careful?--178.99.232.11 (talk) 23:07, 17 April 2016 (UTC)


 * This sounds like it may be a homework problem. WP has several articles that should answer your question for you.  —Quondum 04:16, 18 April 2016 (UTC)


 * We do have an article specifically on the sinc filter. What's "best" mean in this context? What's the sample rate, how do we determine if the signal was created via "undersampling"? Does the Nyquist rate have anything to do with it? Are you concerned about aliasing? These might be good questions to ask yourself, and also might be good articles to read. If this is not a homework question, please explain in more detail what you're confused about and what you're trying to do. Cheers, SemanticMantis (talk) 14:46, 18 April 2016 (UTC)


 * Im thinking of buying a Digital Storage Oscilloscope. Do they have anti aliasing filters on the front end? Signals seem to displayed on the screen by dot joining the data points. Some scopes have a sinx/x filter that can be employed. If I have an under sampled signal (ie with components above half the sampling frequency) and I turn on the sinx/x reconstruction filter, what sort of display will I get> I assume it wont be correct, but what will it look like. Maybe this Q should now be moved to either the computing desk or the science desk??--178.99.232.11 (talk) 16:23, 18 April 2016 (UTC)
 * Sorry, it did look like a homework question at first. I don't know for sure what your undersampled sinc filtered reconstruction will look like compared to the original signal, and I don't have time right now to check or do the math. I think some digital oscs have anti-alias filters and some don't. Rather than post a whole new question, you can try recruit new eyeballs just by posting a new header on the science/computing desk a with a link to this discussion, that way all the responses will be in the same place. I think that it should be fairly straightforward to produce your thought experiment purely digitally, maybe even only using Audacity_(audio_editor). SemanticMantis (talk) 20:36, 18 April 2016 (UTC)
 * FWIW, the question didn't look like HW to me. Sometimes I feel the HW card is being pulled a bit too liberally here. -- Meni Rosenfeld (talk) 20:46, 18 April 2016 (UTC)
 * We do see HW questions verbatim, and lack of context makes it difficult to judge. I should have invited a description of the context – apologies for that.
 * If the sampled signal contains no components above the Nyquist frequency and in-band signals are not distorted, a sinc reconstruction filter will give a theoretically perfect display of the original signal. All decent digital storage scopes should have a good anti-aliasing filter (check the specs), but its BW will not extend to the Nyquist frequency, so frequencies above say 70% of the Nyquist frequency may be distorted.  Any aliasing (signals above Nyqist) in the original will produce significantly divergent traces: the power in the error signal (between original and displayed) will be double the power in the portion of the signal above Nyquist frequency, but usually this will not manifest due to an anti-ailiasing filter on a scope.  (Anti-aliasing filtering can be rather good and have a BW essentially up to Nyquist if the signal is highly oversampled and then digitally filtered and subsampled – I've seen this for scopes aimed at audio.)
 * There is another factor to consider with a digital scope display: at high nominal sampling frequencies, the trace may be reconstructed from multiple passes. For example, if you are examining a signal with a 100 MHz nominal sampling rate, the scope may actually have an anti-aliasing filter for the Nyquist frequency of 50 MHz (with a bandwidth of say 30 MHz), but may actually sample at 12.5 MHz with control of the sampling phase on each of 8 passes.  If the original signal is not repeating accurately over all passes (including if it just has a lot of in-band noise or if the trigger point has jitter), reconstruction (with or without sinc reconstruction filter) can make one think that the signal is very different from what it really is, so one needs to understand the scope.  My comments may be quite dated though.  —Quondum 16:42, 20 April 2016 (UTC)