[sdiy] Digital filtering (Oversampling and downsampling)

[cheater cheater]

Huh?

Oh, are you saying the flux capacitor connects between the cyclotron
and the Z-Machine via the quantum loopback doohickey?

;o)

D.

On Tue, Aug 4, 2009 at 4:12 PM, Andy Eakin<aeakin1 at matrixblues.com> wrote:
> Tom Wiltshire wrote:
>>
>> Hi All,
>> <mega snip>
>>
>> Is this really true? How far does this go? Would I do better still trying
>> to run at 192KHz?
>>
>> Balancing these competing demands without a lot of previous experience
>> seems to be very difficult and very much an art not a science. If anyone has
>> any useful experience or pointers to offer, I'd be grateful for any help I
>> can get.
>>
>> Thanks,
>> Tom
>
> Tom,
>
> I will qualify this with 3 things, First, I am not a "practicing" EE
> although I do have a pretty sheet of paper from quite a few years ago that
> mentions something about Electrical Engineering. Second, I always sucked at
> Calculus.  Third I am still a newbie a teh list.  But follow my exercise (or
> excise) and lets think this out.
>
> So, lets back up and look at the issue of generating and downsampling a
> generated waveform.  I truly believe that this falls right into the art of
> math rather than any defined rule set.
> It would stand to reason that in any given simple waveform being generated,
> you would know in advance the point at which your 96k or 48k would be the
> middle ground (notice I did not say mathmatical middle) and give the least
> amount of artifacts. This really implies a basic Fourier Series. In this
> case a Time limited Fourier Series can be used and reused  as long as there
> is no change in the x or y axis, but even then you would "know in advance"
> the appropriate transformation to apply to the existing dataset to be able
> to maintain a very smooth waveform with little or no induced artifacts.
>
> Ahh, but this is the real world and I am assuming that a nice clean ramp,
> square or sin is not in the plans for this device.  So lets look at the
> "art" side of things.  With a complex waveform, we are in Nobel Prize
> Territory when it comes to the appropriate way to handle this.  It further
> stands to reason stands to reason that in the 8 samples of section or point
> "B" (where you are looking at "A" as being the previous 8 samples and "C" as
> being the next or upcoming samples we should have the necessary data be able
> to derive an approximation of the appropriate data points for our newly
> downsampled waveform.  Unfortunately, without delving into quantum formulae
> (sucked at those too BTW) we cannot predict  points A , B and C in our new
> waveform with any degree of accuracy PERIOD. It is simply impossible to
> obtain an errorless calculation without knowing the full dataset before and
> ahead of the point you are creating.  Even if you looked at datapoints "A-1"
> and "C+1" you could only get as accurate as your store of previous data is
> large and your latency will allow you to go into the "future".
>
> Sorry about that was a book, and my brain feels better after the exercise :)
> .
> So this bears a few questions.  First where does the waveform go after it is
> downsampled?  Is there any chance of jitter or error being injected prior to
> its sweet (or sour) sound reaches the analog realm?  What kind of tolerance
> for artifacts do you have in this system? Did you leave the iron on?
> (uncertainty principle) How much DSP power do you have?  and What is your
> latency Tolerance?
>
> Your DSP may have Fourier commands built in or included in its codebase.
>  Have you tried those?  Does your DSP have an anti-aliasing routine in its
> library?
>
> /TLDR -- It Depends.
>
> Andy E
>
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