[music-dsp] Re: Declipping

[Yaakov Stein]

> With comments like "of course you can't do that in the real 
> world" and the quotes surrounding "play them back" in the 
> snippet you quoted, I can't believe that you don't see that I 
> was presenting an argument conceptually.

So was I.

I wasn't trying to claim that your argument is theoretically correct
but can not be implemented, I was just saying that it is theoretically
incorrect.

> 
> Here, while you're at it you can email Julius O. Smith and 
> chastise him about this one, which I posted in an earlier message:

I don't care if Julius Cesar used the same argument.

For that matter, I am sure that you can find many uses
of complex valued signals, but when you start saying
that the imaginary part is "really there" and we should
be looking for it, that's where I must disagree.

> Wrong, wrong, wrong

I am glad I have convinced you.

> I'm still eager to read your explanation of why we insert zeros to
upsample.

I already explained it in depth, but let's try again.

When increasing the number of samples in the same amount of time,
we have to put in something. By putting in a constant value
(zero or anything else, but use the average signal value for best
numeric stability) you are sure to add components only in the
newly created high parts of the spectrum. This is clearly no longer
the "same signal", but agrees precisely with the original signal's
spectrum in the bottom part. So by LP filtering we retrieve a signal
that perfectly agrees with the original signal over the entire spectrum.
By the perfect reconstruction characteristic of the FT
this signal is the only signal that can be called "the same" as 
the original signal
- and this signal has interpolated values (not zeros!) in the
new sample places.

Clear enough now?

Jonathan (Y) Stein