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Plesiochrounous Audio re-sampling D/A > filter > A/D

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June 7, 2005 11:43:43 AM

Archived from groups: rec.audio.pro (More info?)

I have a question about PLESIOCHROUNOUS re-sampling of audio.


It was mentioned in another thread that simply deleting or repeating a
sample now and then is a poor solution because it adds clicks.


It was mentioned that linear interpolation is not ideal. Why? Because
it adds noise? or distortion?


I presume the "ideal" digital solution is to use a higher order
interpolation algorithm. Is this correct?


And here is my real question. I understand that re-sampling by
converting the signal back to analog, reconstruction filtering, then
re-sampling in a A/D is considered a kludgey. But assuming we didn't
care that it was kludgey and the A/D and D/A are good, in terms of
audio quality, how does the D/A > A/D method compare to the other
methods mentioned above in terms of audio quality?


Is the D/A >A/D method theoretically equivalent to a very high order
digital interpolation? It seems we need to compare the operation of
the digital interpolation filter vs the operation of the analog
reconstruction filter.


In practice, how complex of a digital interpolation filter would be
needed to get audio performance that was as good or better than can be
obtained using typical D/A > A/D.

thanks
Mark
Anonymous
June 7, 2005 4:18:30 PM

Archived from groups: rec.audio.pro (More info?)

Mark wrote:
> I have a question about PLESIOCHROUNOUS re-sampling of
audio.

> It was mentioned in another thread that simply deleting or
repeating a
> sample now and then is a poor solution because it adds
clicks.

Yes, just naively adding or removing samples can cause
clicks.

> It was mentioned that linear interpolation is not ideal.
Why?

When interpolation is done, it really implies some kind of
filtering. When you are resampling, generally the sharpest
kind of filtering is desired. Linear interpolation won't
give you the sharpest kind of filtering.

> Because it adds noise? or distortion?

Because it doesn't remove the most noise and distortion with
least effect on the signal.

> I presume the "ideal" digital solution is to use a higher
order
> interpolation algorithm. Is this correct?

See former comments about filtering.

> And here is my real question. I understand that
re-sampling by
> converting the signal back to analog, reconstruction
filtering, then
> re-sampling in a A/D is considered a kludgey.

Right, because it includes an unecessary trip through the
analog domain.

> But assuming we didn't
> care that it was kludgey and the A/D and D/A are good, in
terms of
> audio quality, how does the D/A > A/D method compare to
the other
> methods mentioned above in terms of audio quality?

See former comments about the analog domain. The analog
domain has a number of undesired attributes including
nonlinear distortion and reduced resolution.

> Is the D/A >A/D method theoretically equivalent to a very
high order
> digital interpolation?

It can be if the converters are good enough.

>It seems we need to compare the operation of
> the digital interpolation filter vs the operation of the
analog
> reconstruction filter.

No, you have to notice that big readily-avoidable trip
through the analog valley of the shadow of death, noise and
distortion. ;-)

> In practice, how complex of a digital interpolation filter
would be
> needed to get audio performance that was as good or better
than can be
> obtained using typical D/A > A/D.

In the digital domain, its all just numbers and code. It's
relatively cheap to stack processing and data as high and
deep as is necessary to do the work with the precision you
want. If you do it with dedicated hardware, it costs money
and you have limited parameter choices.

One other thing most trips from digital to analog to digital
are ansynchronous or potentially so. In contrast, if you
stay in the digital domain, synchronous operation which can
be beneficial, is almost automatic.

One other thing - if you do resampling in the analog domain,
it has to happen in real time. If you have the CPU
horsepower, and we often do with modern computers, a lot of
processing can be done in a tiny fraction of real time. Is
your time worth anything?
Anonymous
June 8, 2005 12:22:07 AM

Archived from groups: rec.audio.pro (More info?)

"Mark" <makolber@yahoo.com> wrote:

>It was mentioned that linear interpolation is not ideal. Why? Because
>it adds noise? or distortion?

Given a sufficient number of digits noise is no problem in the digital
domain. Linear interpolation simply adds distortion. If you look at
a sample on its way from the D/A converter to the low pass filter (lpf)
and to the analogue world: Each sample is converted to a sin(x)/x
function by the lpf. The function is infinite in length (in theory)
and each sample adds another (tiny) sin(x)/x to the analogue output...

>
>I presume the "ideal" digital solution is to use a higher order
>interpolation algorithm. Is this correct?

.... thus the best way to interpolate is to use sin(x)/x as function.

>In practice, how complex of a digital interpolation filter would be
>needed to get audio performance that was as good or better than can be
>obtained using typical D/A > A/D.

Changing the sample rate in the digital domain usually involves a set
of several lpf and adding/deleting samples. Lets look how 48 kHz to
44.1 kHz resampling is (usually) done: As 480/441 is not an integer
number we need to first "interpolate" to 48*441 kHz and the decimate
to the required sample rate. As the output sample rate is lower than
the input sample rate a low pass filter is needed in the first step
to cut all information above 22.05 kHz. An increase in sample rate
(interpolation) by a factor of 441 is achieved by inserting 440
zero value samples between each input sample.
This step will add distortion, of course, but way above 22.050 kHz.
Thus the next lpf step will remove it. In this step we have to adjust
the loudness as well to get close to the original level. After that
we simply have to discard 479 samples in every set of 480 samples
and are done. [This can be done without introducing any distortion
as those samples are identical due to the lpf of the first step.]

Norbert
!