Re: IM distortion: why related to level?

On Oct 23, 11:48 pm, MRC01 <m...@xxxxxxxxxxxxx> wrote:
That's one reason why, for example, sample rate conversion
algorithms ALWAYS start FIRST with an anti-imaging filter
(even though you might not think it necessary), it does
the conversion, and then it has an anti-aliasing filter,
even though everything is done in the digital domain.

It depends on the goal. If the goal is to reliably produce the closest
thing to a square wave that 44.1 kHz samples allow, then what you
describe makes sense. But if the goal is to test how well the DAC
interprets a difficult waveform then one *should* use the simpler
mathematically pure square wave that you described. Theoretically, an
ideal DAC should output a proper looking square wave when fed that
signal. It should be able to filter out everthing > 22.5 kHz with
minimal passband distortion.

No, that's what you're not getting: The waveform I described is
NOT "mathematically pure;" It's already broken BEFORE it
gets to the DAC: because it is discrete time sampled, and
because it was NOT band-limited before it was generated,
it already contains all of the aliases folded down into the
baseband.

Nothing in the real world is perfect; one
should expect to see some distortion, but the goal is to compare the
distortion generated by different DACs.

Then the step-generated square-wave I described is NOT
the way to do it, because it is intrinsically distorted before
it hits the DAC.

Let's try a different approach: whatever code you are using
to generate the waveform can be viewed as THE analog-to-
digital conversion process for that waveform. The code IS
sampling a waveform. And to prevent ANY aliases from
finding there way into the sampled stream, the waveform
MUST be low-pass filtered to less than 1/2 the sample rate
BEFORE sampling.

Therefore, a sample sequence of the type I described first,
where you have some number of samples at some positive
level, followed by the same number of samples at the
same negative value, IS ALREADY BROKEN in that it
was not properly anti-alias filtered before sampling.

A 10 kHz waveform generated this way will have, in
it's "pure mathematical" form, harmonics at 30 kHz,
50 kHz, 70 kHz and so on. In that sampled stream,
those harmonics will already be folded back to 14.1 kHz,
5.9 kHz, 28.2 kHz and so on. Those aliases ARE ALREADY
IN THE SAMPLED STREAM. A PERFECT DAC could NEVER
filter them out: they're within the passband of a perfect
anti-imaging filter.

Now, what would that same 10 kHz square wave really look
like in the sampled stream if captured by the perfect ADC?
Well, since 30 kHz and everything else above the Nyquist
frequency gets filtered, the sampled stream would consist
ONLY of the sampling of a 10 kHz SINE wave.

Let's repeat, a step-generated sampled square wave is a
BAD test for a DAC, becuase that sampled stream is already
heavily distorted with the aliases, because the Nyquist
criteria was violated by the very sampling process used to
generate it. If a DAC playing such a waveform sounds
distorted, the DAC is doing its job correctly, because
the sampled waveform is distorted.

It's far from intuitive, to be sure. But it's another case
where intuition about things is simply wrong.

.

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