Recreating Undersampled Data

On 5/19/2017 3:12 PM, Steve Pope wrote:
> rickman  <gnuarm@gmail.com> wrote:
>
>> On 5/19/2017 2:58 AM, Steve Pope wrote:
>
>>> rickman  <gnuarm@gmail.com> wrote:
>
>>>> On 5/19/2017 1:20 AM, Steve Pope wrote:
>
>>>>> Yeah, you know, one of the basics of sampled signals is that when
>>>>> you uniformly sample a signal, the components of that signal then
>>>>> become aliased repeatedly up to infinity.
>
>>>> Is it not true that a sampled digital signal has no content above 0.5 Fs?
>
>>> In discrete time, the frequency components are defined from 0 to 0.5 Fs.
>>
>> Not defined... that is what exists.
>
> Surely an ontological question is beyond the scope of this discussion.
>
>> Any information about signal frequencies above 0.5 Fs has been lost.
>
> Really? Which version of the sampling theorem are you using?
>
>> You have acknowledged the signal is *not* there in the ADC data.
>
> No, I have not.  Specifically, a signal in a narrow band around
> 2.0625 MHz is definitely entirely contained in ADC data sampled
> at 1 Ms/sec.  Because, Nyquist.
>
>>>> You can't filter something that isn't there.
>
>>> It's there, dude.
>
>> It is not there as you have acknowledged above.  You can recreate it,
>> move it or whatever, but once the signal is aliased by under sampling,
>> the information required to reconstruct it is lost.
>
> 100% false.
>
>>> I've explained several times how to get it
>>> and why it's there.  As I said, this is basic sampled signals theory.
>
>> Above you acknowledged the ADC output does not contain any information
>> above 0.5 Fs.
>
> Do not tell me I said things that I have not said.
>
>> The only reason why you can reconstruct the signal at 2.065 MHz is
>> because there is no interfering signal when it is aliased down to 0.065
>> MHz.
>
> Finally we can agree on something.
>
>> In the general case once the signal is aliased down it can no
>> longer be separated from other signals aliased to the same frequency.
>> So you use this special knowledge of this particular signal to
>> reconstruct it by any of various means.
>
> *Any* sampling of a signal that is valid per the Nyquist criterion
> is using "special knowledge" of the signal, and this is no different
> from the general case.
>
>> I was visualizing this in my mind and realized the adjustment to the
>> time base is equivalent to up sampling and filtering.  I won't try to
>> reconstruct the filter this implies, but I bet it ends up be very
>> similar if not equivalent to what you are proposing.
>
> We very likely agree here, if I knew the details of your "adjustment
> to the time base".

We are going in circles, repeating ourselves.  I say sub-sampling looses 
information and you say it does not.  You snip parts of my posts that 
you don't wish to address, so there is no point in discussing it 
further.  This conversation no longer has a heart beat.  I'm calling 
code...  5:06 PM

-- 

Rick C

On Fri, 19 May 2017 11:54:47 -0700, makolber wrote:

> On Thursday, May 18, 2017 at 4:09:29 PM UTC-4, eric.j...@ieee.org wrote:
>> On Thu, 18 May 2017 12:42:18 -0700 (PDT), makolber@yahoo.com wrote:
>> 
>> 
>> >
>> >> I'm going to say there are aliases are 0.0625 MHz, and 1 + n *
>> >> 0.0625 MHz for all non-zero integers n.
>> >> 
>> >> 
>> >i think the already mentioned (under)sampling oscilloscope is the
>> >better analogy for this question.
>> >
>> >i.e. the time domain rather than the frequency domain
>> >
>> >an (under)sampling scope doesn't need to know the shape of the
>> >waveform, it needs to know only that the waveform is repetitive.
>> 
>> Ideally it needs to know the frequency, or, better yet, phase lock to
>> it.   Phase locking to a triangle of reasonably known frequency is
>> definitely achievable.
>> 
>> 
> 
> ok true.
> 
> so an under sampling scope can create an accurate picture of the
> waveform from the under-sampled information knowing:
> 1) the waveform is repetitive 2) the exact repetition frequency
> 
> and that's it
> 
> 
> with the restriction that the sub sampling frequency must NOT be a sub
> multiple of the rep rate.
> 
> seems pretty clear in the time domain interesting mental exercise to
> work it out in the frequency domain
> 
> m

Interesting to work it out in the frequency domain, but profitable only 
if you need to for educational purposes, if there are complications, or 
if there's some pendant in the loop who has forgotten that life is a time 
domain phenomenon.

The frequency domain is there to make things easier to solve when they're 
freaking hard to solve in the time domain.  If they're freaking easy to 
solve in the time domain, then going to a bunch of effort to solve them 
in the frequency domain is just a waste of that effort.

-- 
www.wescottdesign.com