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Chris Rehorn's paper about Sinc interpolation

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bdunham7:

--- Quote from: tom66 on February 14, 2023, 02:26:08 pm ---So you would realistically need something like at least a 250MSa/s ADC and design your 100MHz bandwidth to roll off to at least -48dB at 125MHz (6dB/bit rule of thumb for quantisation SNR).  That is a pretty steep filter, but with good design is achievable.

--- End quote ---

Really?  That seems like an extraordinarily difficult task to me and almost certainly more difficult and expensive than simply quadrupling the sample rate. 

tom66:

--- Quote from: bdunham7 on February 14, 2023, 04:53:55 pm ---Really?  That seems like an extraordinarily difficult task to me and almost certainly more difficult and expensive than simply quadrupling the sample rate.

--- End quote ---

So perhaps I had better rephrase:  It is achievable with good design, at some cost.   May not necessarily be done on a 100MHz scope as you note, a faster ADC could be cheaper especially when the tolerance of the required components is, plus any factory calibration.   It would definitely be a steep filter but there are oscilloscope architectures which include similar complexity filters, for instance Siglent 5104X samples at 2.5GSa/s in some channel modes, with a 1GHz bandwidth.  As far as I know and could test there was no obvious aliasing on that scope at the bandwidth limit so it presumptively must achieve something close to -48dB rolloff at 1.25x its input frequency.


--- Quote from: imo on February 14, 2023, 04:08:03 pm ---That is the key message - "if the input signal does not contain frequency content above and beyond the Nyquist frequency".

What type of a signal? A sine/cosine only? Not applicable for a "square wave", for example, imho..

--- End quote ---

Yes and no.  A 100MHz scope is widely understood to be not very useful at looking at square waves >>20MHz frequency, because the components to construct that wave are lost to the bandwidth limit of the instrument, regardless of the ADC sampling rate.  However, if you do acknowledge your instrument has a 100MHz bandwidth limit, then if its ADC filter is correctly designed and it uses correctly implemented sinc interpolation, it does accurately and exactly show the picture of what your signal looks like, up to that bandwidth limit.   I guess the way to see this is if you had an ideal 100MHz CRO and compared it to a 100MHz DSO, a well implemented DSO (with intensity-grading and the like) would show a waveform equivalent to the CRO.

What the real world implications of this are depends on what you are doing with the scope.  Are you using it for looking at square waves?  In theory, there is no upper bandwidth limit for a square wave so... you can never see the true picture, though in practice more than 10-15x the frequency for the scope bandwidth has little additional benefit. 

I suspect the Agilent engineer is writing this from a communications theory background.

bdunham7:

--- Quote from: tom66 on February 14, 2023, 05:31:04 pm ---It would definitely be a steep filter but there are oscilloscope architectures which include similar complexity filters, for instance Siglent 5104X samples at 2.5GSa/s in some channel modes, with a 1GHz bandwidth.  As far as I know and could test there was no obvious aliasing on that scope at the bandwidth limit so it presumptively must achieve something close to -48dB rolloff at 1.25x its input frequency.

--- End quote ---

I have not had the opportunity to test an SDS5104X, but on all the other Siglent models I've seen they just alias away and appear to have a -6dB response at least to 2X their rated BW.  -48dB at 1.25X BW would imply a 144dB/octave rolloff with an analog design.   I'd be interested to know exactly how you tested your example.  The way I would do it would be to compare equal-amplitide 1GHz and 1.5GHz inputs. 

gf:

--- Quote from: bdunham7 on February 14, 2023, 04:53:55 pm ---
--- Quote from: tom66 on February 14, 2023, 02:26:08 pm ---So you would realistically need something like at least a 250MSa/s ADC and design your 100MHz bandwidth to roll off to at least -48dB at 125MHz (6dB/bit rule of thumb for quantisation SNR).  That is a pretty steep filter, but with good design is achievable.

--- End quote ---

Really?  That seems like an extraordinarily difficult task to me and almost certainly more difficult and expensive than simply quadrupling the sample rate.

--- End quote ---

A 7th order elliptic filter is likely realizable, but I guess you won't like its impuse and step response.

Btw, at the end you can never see the original signal if is not band-limited in the first place. If you need an anti-aliasing filter in order to enable "perfect reconstruction" from the samples, then you still cannot reconstruct the original signal, but only the filtered one.

tom66:

--- Quote from: bdunham7 on February 14, 2023, 05:55:15 pm ---I have not had the opportunity to test an SDS5104X, but on all the other Siglent models I've seen they just alias away and appear to have a -6dB response at least to 2X their rated BW.  -48dB at 1.25X BW would imply a 144dB/octave rolloff with an analog design.   I'd be interested to know exactly how you tested your example.  The way I would do it would be to compare equal-amplitide 1GHz and 1.5GHz inputs.

--- End quote ---

Been a while as we had it on loan as a demo unit pre-COVID, but I ran a DDS into it and swept up to about 700MHz on a square wave (IIRC that was the limit of our generator for square)  then looked at the FFT response to see if there were any obvious aliases as I moved the frequency up and down.  None appeared, though I suppose it's possible this test didn't capture real aliasing.

We've got an SDS6000 on loan (the 2GHz, 4 channel one) coming next week which will be interesting to test.

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