16/44 vs. 24/96 Format Comparison

[Patrick Dixon]

Only right at the nyquist rate or higher do you get garbage.

Not exactly garbage - just aliasing.

[seanadams]

If you have a 20 KHz square wave that's bandwidtch limited to 1 MHz and pick a Nyquist frequency of 22.05 KHz, you've picked too low a Nyquist limit to accurately reproduce the waveform. But if you pick a Nyquist frequency of above 1 MHz, the waveform can be reproduced exactly.

Right. That's real likely.

?!?!?

Pat, I don't really get what you're saying here. Is it that you believe the Shannon Nyquist theorem is incorrect, or do you believe that a band-limited square wave can not be expressed as a finite sum of sine waves, all below said band limit? This is pretty fundamental stuff... the latter statement is true simply by _definition_ of "band limited".

Round the numbers to make it easier to see.
20kHz square wave, sample at 40kHz.
result is 1, -1, 1, -1, 1, -1, ...

You've chosen an especially poor example here because in this case 20KHz is at exactly the Nyquist frequency. For waves at this exact frequency there are in fact an infinite number of different phase/amplitude combinations which could yield a given set of samples.

But that aside, the important point here is that you've forgotten the step where said 20KHz square wave is filtered before sampling. When you remove content above 20KHz, what you end up with is a perfect 20KHz sine wave. That is really ALL there is left. A square wave is comprised of a sine at its fundamental frequency, plus a sine at every odd harmonic above that: sin(x) + sin(3x)/3 + sin(5x)/5 + sin(7x)/7 etc. Try graphing it.

This is the basis of what opaqueice stated earlier. The ONLY difference between a 20KHz square and a 20KHz sine is at 60KHz and up. Band limit them and they're identical.

Feed it through a DAC and you get a 20kHz sine wave.

And that is exactly what went into the ADC!

[pfarrell]

seanadams wrote:
> Pat Farrell;231200 Wrote:
>> Right. That's real likely.
> Pat, I don't really get what you're saying here. Is it that you believe
> the Shannon Nyquist theorem is incorrect, or do you believe that a
> band-limited square wave can not be expressed as a finite sum of sine
> waves, all below said band limit? This is pretty fundamental stuff...
> the latter statement is true simply by _definition_ of "band limited".

I believe in Shannon.

I think we are talking past each other, probably in violent agreement.

I don't believe that real square waves happen. They never happen in
music, and even with a signal generator, the LRC network of any wiring
will round off the sharp edges to some degree. You use a signal
generator capable of 100kHz or more to make even a vaguely square 20kHz
square wave.

The resulting almost square wave is more clearly a sum of high frequency
sine waves. With rounded edges, you don't need to go to infinite
frequencies and infinite sums.


> Pat Farrell;231200 Wrote:
>> Round the numbers to make it easier to see.
>> 20kHz square wave, sample at 40kHz.
>> result is 1, -1, 1, -1, 1, -1, ...
>>
>
> You've chosen an especially poor example here because in this case
> 20KHz is at exactly the Nyquist frequency.

Yes, its poor, I picked it and the phase points being sampled on purpose.

Not much changes if you sample that same square wave at twice the rates,
which I also showed.

> But that aside, the important point here is that you've forgotten the
> step where said 20KHz square wave is filtered before sampling. When you
> remove content above 20KHz, what you end up with is a perfect 20KHz sine
> wave.

Not me, its others that are talking about 20kHz square waves being
important.

There has been a lot of pseudo math in this thread. That's why I posted
up thread that the keys are the mathematics of Taylor series and
Maclaurin series, which predate Shannon's theory.


> This is the basis of what opaqueice stated earlier. The ONLY difference
> between a 20KHz square and a 20KHz sine is at 60KHz and up. Band limit
> them and they're identical.

That may be true, but I sure didn't read it that way.

Even at 60kHz sampling, your square wave ain't gonna be square when you
recreate it.

If you look at music, there is damn little signal above 10kHz. A few
overtones, most of them way down in level relative to the fundamentals
in the 200 to 3,000Hz range.

[opaqueice]

> This is the basis of what opaqueice stated earlier. The ONLY difference
> between a 20KHz square and a 20KHz sine is at 60KHz and up. Band limit
> them and they're identical.

That may be true, but I sure didn't read it that way.

Even at 60kHz sampling, your square wave ain't gonna be square when you
recreate it.

I said

You're very confused about this. It's not a "common misunderstanding". Just ask yourself what the difference is between a 20 kHz square wave and a perfectly smooth 20 kHz sine wave.

Answer - a 60 kHz sine wave (plus higher frequencies). So if you can hear 60 kHz, you'll know the difference.

which is true. Take the difference between a 20 kHz sqaure wave and a (normalized appropriately) 20 kHz sin wave and you get a series of higher frequency sin waves starting at 60kHz. That's a result of basic Fourier analysis (we don't even need to touch the 20th century for this), and (since we can't hear above around 20kHz) it explains why if you DID go to the trouble of producing a 20kHz square wave it would sound exactly like a 20kHz sin wave.

I'm not sure which part you don't agree with.

[pfarrell]

Take the difference between a 20 kHz sqaure wave and a (normalized appropriately) 20 kHz sin wave and you get a series of higher frequency sin waves starting at 60kHz. That's a result of basic Fourier analysis (we don't even need to touch the 20th century for this), and (since we can't hear above around 20kHz) it explains why if you DID go to the trouble of producing a 20kHz square wave it would sound exactly like a 20kHz sin wave.

I'm not sure which part you don't agree with.

Who do you, opaqueice mean by "you".

http://forums.slimdevices.com/showthread.php?t=38813
tries to bring some sense to this general discussion.

As mentioned in the alternative thread, pass the square wave through the proper filter, you have a sine wave, which you can sample. And duh, when you reproduce it, you get a sine wave.

If I could, I'd set follow-ups about sample theory, square waves, Fourier, Taylor, etc. to

http://forums.slimdevices.com/showthread.php?t=38813

[opaqueice]

Who do you, opaqueice mean by "you".

Can I buy some of whatever you're smoking? It might make it easier for me to understand this exchange....

[pfarrell]

I don't see any point in personal attacks. They are uncalled for.

[opaqueice]

I don't see any point in personal attacks. They are uncalled for.

Please accept my apologies. It was intended as a joke, not as any kind of attack.

Honestly, I really had (and have) no idea what you were asking there, or really what your point was earlier. But I guess we've failed to communicate enough times in one thread, so maybe we should let it die.

[pfarrell]

opaqueice wrote:
> pfarrell;231306 Wrote:
>> I don't see any point in personal attacks. They are uncalled for.
>
> Please accept my apologies. It was intended as a joke, not as any kind
> of attack.

Accepted.





--
Pat Farrell
http://www.pfarrell.com/

[amey01]

What do you mean by "Nyquist criterion" if not that frequencies above 22kHz (or 18 for that matter) are inaudible?

It's not a question of whether or not they are audible. It is whether or not they have an *EFFECT* on what you hear!

It can be scientifically proven that even if you cannot hear it, it can have an effect on what you can hear.