Please excuse my ignorance on DAC design and related digital filtering.
While I do believe I understand the signal theory part and the way the
DACs fundamentally work I don't know a lot about how digital filters in
these things are actually implemented.

JohnSwenson wrote: 
> The amplitude of the alias is determined by the "height" of the "stair
> step" in the signal.
> 
Which "stair step"????
In the filter function? 
I mean... there are no "stair steps" in the sampled signal itself
(unless you create artificial samples for oversampling which, of course,
are not "stair steps" but simply potentially wrong samples creating
harmonics....)

I know... all those hifi mags and high-end manufacturers always show
this stair-step graph over the sine wave but you and me know that's
nonsense and that sine wave in that example can actually be perfectly
reproduced from only two samples...

Now, here's what I don't get:
> 
> The filter adds steps in between the originals steps, because of the
> increased samples and the increased bit depth the height of the steps is
> much less, thus producing much lower amplitude aliases.
> 
But to do that, it needs to know _how_ to interpolate to get a "better"
interpolation value.
I mean.... in that nonsensical sine wave image from the hifi mags things
look easy, but in real life the wavform looks something like this
https://soundcloud.com/barbnerdy/lets-go-dancing-june-2013

So if your first sample has a value of, say, "50", and the second one
has a value of, say, "100", you have no way to say that "75" is a good
interpolation value. The "correct" value might as well be "4096" or "0",
unless you do a full spectral analysis over the resulting signal you
just can't know whether "75" is any better than just duplicating "50" so
a linear or logarithmic or whatever arithmetic interpolation will with
all likelihood just as bad and the chances for it improving your signal
are exactly the same as the chances for worsening it.
On average, you just add the same amount of noise as with simple
duplication.

Unless, of course, your interpolation filter _does_ some sort of
spectral analysis but then that's quite a task which is why I asked what
exactly sox is doing to interpolate...

> 
> The reason to do the digital filtering at all is that for 16/44.1 the
> stair steps are large
> 
But only due to oversampling, right?. I still don't get how that affects
NOS DACs.

I thought NOS DACs will have all the wrong excess signal beyond your
cutoff frequency still in there and you need to use analog filters to
get rid of it or rely on intermodulation filters in your power amp?

> 
> Now let's look at what happens with the signal upsampled to 176.4, the
> aliases start at 88.2.
> 
Ah... OK, so the idea here is that instead of having an alias above your
cutoff frequency you just get white or pink noise which can't
intermodulate with your actual signal?

The part I still don't understand is how the interpolation actually
reduces the aliasing. Because if it doesn't, wouldn't you just get the
same amount of aliasing in your upsampled signal as you would have in
any oversampled signal?

How does the interpolation filter do something else than the low-pass
you would usually use for anti-aliasing and still be effective?

Or does it just add more noise so that... 
> 
> Now the fun part is to do this filtering in such a way that it preserves
> the flavor of the original recording. 
>



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