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#19007 - 11/14/02 01:00 PM Re: DSP based time alignment/EQ gizmo
charlie Offline
Desperado

Registered: 01/14/02
Posts: 1176
Have a lookit this:

Nyquist theorem. The Nyquist theorem states that if a signal V(t) does not contain frequencies higher than fs/2 (where fs = 1/Ts), then it can be fully recovered from its sampled values V( nTs) at discrete times tn = nTs ...

http://www.digital-recordings.com/publ/pubrec.html

I want to move to theory 'cause everything seems to work there. In reality the higher than x2 the sample rate is the easier it is to implement. I suspect a x2 system might actually be impossible to build, but I'm not enough of a math genius to prove it.
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#19008 - 11/15/02 06:51 PM Re: DSP based time alignment/EQ gizmo
soundhound Offline
Desperado

Registered: 04/10/02
Posts: 1857
Loc: Gusev Crater, Mars
There seems to be missing one very important point in this discussion of the AD/DA process.

The final step in the digital to analog conversion process always includes a low pass filter between the Nyquist frequency and the word clock frequency i.e. for a 44.1K system, between ~20Khz and 44.1Khz.

This does two very imprtant things:

It strips off the word clock (44.1K etc).

It removes ALL harmonics of the audio above the Nyquist frequency.

Thus - a 20Khz tone stripped of all of it's harmonics equals a pure SINE WAVE.

The raw output of the D/A converter before the low pass, for a frequency approaching the Nyquist frequency (20Khz) is an approximation of a square wave, not a triangle wave, due the sample and hold stage.

[This message has been edited by soundhound (edited November 15, 2002).]

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#19009 - 11/15/02 09:30 PM Re: DSP based time alignment/EQ gizmo
charlie Offline
Desperado

Registered: 01/14/02
Posts: 1176
Sure enough.

Actually I intentionally skipped a lot of steps in interest of clairity, at sacrifice of detail. This is what I was generalizing when I said "The simple 'connect the dots' shape contains frequencies higher than the Nyquist frequency. Or we could say the D/A step produced these frequencies, however we want to look at it. In any case, they will be removed in the next step."

Not technically complete, but I know how much I hate it when I ask a question and get an overly detailed answer to a question. It's hard to know where to draw the line.

One item that is also very often ignored or forgotten is the low pass before the sampling step.
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