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Topic: Oversampling Better? (Read 12140 times) previous topic - next topic
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Oversampling Better?

Reply #25 –
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You example at fs/2 is right. It is not possible to record fs/2. Only frequencies strictly inferior to fs/2.

No, it's *sometimes* possible to get fs/2 depending on the phase - a signal alternating between +1 and -1 is definitely fs/2 - and if you amplitude modulate any signal with this +1/-1 alternating signal, you "invert" the spectrum as you'd expect (so signals at 0.1fs get shifted to 0.4fs, etc.).

sorry for staying so off-topic, but....

yeah, i see what you're saying, but that wasn't my issue. my problem was that, given a signal at fs/2, you couldn't ever tell what the actual amplitude of the signal was, since you'd be lacking the phase information. as pio pointed out, my problem was that i was only looking at the fs/2 frequency. at anything else, you get beats---amplitude of the beats is close to the amplitude of the signal (it may be equal, but my intuition about discrete signals is rather poor), and the frequency of the beats is the difference between the sampled frequency and the sampling frequency, unless i'm terribly mistaken...

so here's my next question: how do you tell the difference between a signal with an oscillating amplitude at fs/2 and one with constant amplitude at some other frequency. or is there no difference?

Oversampling Better?

Reply #26 –
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how do you tell the difference between a signal with an oscillating amplitude at fs/2 and one with constant amplitude at some other frequency. or is there no difference?

The difference is that the oscillating signal has some frequencies above Nyquist's limit, while the constant one has not.

In fact, the mathematical concept of frequency is a bit different from what the intuition suggests. A given frequency is a sinewave that never starts and never stops, and never changes its amplitude.
If we modulate the amplitude of a sinewave, we get a new wave. Its mathematic "period" is changed. It repeats itself only after the amplitude has been completely changed.
Say that we modulate a 22050 Hz wave in a sinusoidal way, one time per second. The new wave is a function of time that repeats itself each second. Therefore its fundamental frequency is 1 Hz, and the harmonics are 2,3,4,5 etc Hz. In fact nearly all its harmonics have an amplitude of zero.
Only the 22049 and 22051 Hz harmonics have an amplitude different of zero.

Thus 22049+22051 Hz is the same as 22050 Hz + amplitude modulation each second. They are two different ways of writing the function of time that the wave is. But only the first one describes it in sum of pure frequencies. The second one describes an altered frequency.

Then the sampling theory comes into play. A sampled signal such as this one can be generated by an infinity of different waves. For example, 22049+22051+88200 Hz. The 88200 component will not affect the sampling at 44100 Hz, the result will be the same as 22049 + 22051. In the same way, the 22051 Hz component only affects the amplitude of the result. A single 22049 Hz sine gives exactly the same shape when sampled at 44100 Hz.
That's the meaning of "complete description" of frequencies under 22050 Hz. Frequencies above are only partially described, because different frequencies can give the same sampled result. I think also that to get a complete description, the original signal must not have any frequency above 22050 Hz. Then, there is a unique way of reconstructing the original wave from the sampled one.

In our example, the reconstruction is a steady 22049 Hz sine. I can't be an oscillating 22050 Hz one, nor even, say, an oscillating 22049.9 Hz one, because this have frequency components above 22050 Hz, and this possibility has been discarded when the 44100 Hz sampling rate was chosen.

Oversampling Better?

Reply #27 –
yeah... thanks for the excellent, very detailed response. i just realized it was a stupid question, though...

Oversampling Better?

Reply #28 –
Thanks too for the very detailed answer, but why I (and the others persons) hear the difference?

Oversampling Better?

Reply #29 –
Let me guess,  Marcan,  you and Neck are using some late SB soundcards?

The reason you hear those downward tones are becase they are false tones
being created by the resampling process that some cards have to do,  since they
do not operate at 44.1Khz. 

SB Live and Audigy1 and some others are like this, they run at 48 Khz internally,
so they have to resample up to 48..  and they don't do it very cleanly. 

If you run at 48Khz to begin with, you don't go thru the process,  and don't have
the errors..

Hope it helps..

Jon

Oversampling Better?

Reply #30 –
Thanks Jon.

My DAC is an Emagic emi2|6 (professional). I can choose the internal conversion rate (44.1, 48, 96).

We can easily hear the difference on professional equipment (Genelec, Yamaha NS10, Quested, ...).

Oversampling Better?

Reply #31 –
Marcan, burn this sweep on a CD and try it in a CD player. I don't understand how your soundcard work !

Oversampling Better?

Reply #32 –
Pio, the sweep sound isn’t really important. When we hear a track, we can easily hear a difference between a 44.1 and 96 khz conversion. The high frequencies are really better.

I think the difference is because the anti-alising filter is higher and because the high frequencies are reproduced more naturally.

Oversampling Better?

Reply #33 –
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It gives poorer time-domain resolution though.

What does?  88.2 kHz has better time-domain resolution than 44.1 kHz.

Yes. But if you take a 44.1kHz sampled signal, and let the DAC do the reampling, then a more gentle filter may be used, which would give better time domain resolution. The resampling in Cool Edit, set to a reasonably "high quality" setting will give excellent frequency response, but poor temporal accuracy. This is the "theoretical" best result, but in practice a compromise between time and frequency domain accuracy may sound better.

(Even this statement is misleading - the theoretical best resampling which Cool Edit almost manages is "perfect" in both time and frequency domain, within the limits of the system. Unfortunately, these limits may give infinite ringing at 22.05kHz - that's what a compromise may be better!)


Cheers,
David.

http://www.David.Robinson.org/

Oversampling Better?

Reply #34 –
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Pio, the sweep sound isn’t really important. When we hear a track, we can easily hear a difference between a 44.1 and 96 khz conversion. The high frequencies are really better.

I think the difference is because the anti-alising filter is higher and because the high frequencies are reproduced more naturally.

If the audible high frequencies are better sampled at 96k than 44.1k, then there's something wrong at 44.1kHz!

But isn't this the whole point - we live in the real, imperfect world. 44.1kHz should be enough - but with real world (even very good) equipment, 96kHz sounds better.

It doesn't prove that Fourier or Nyquist were wrong, or that we all have Bat-like hearing. It just shows nothing is perfect.

Maybe!

D.

Oversampling Better?

Reply #35 –
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If the audible high frequencies are better sampled at 96k than 44.1k, then there's something wrong at 44.1kHz!

If information > 22 KHz is really inaudible, then there has to be something really wrong in any system to sound so different from 96 KHz. Marcan, As Pio suggests, try burning the sweep and play it in a good cd player.

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But isn't this the whole point - we live in the real, imperfect world. 44.1kHz should be enough - but with real world (even very good) equipment, 96kHz sounds better.


I don't think this can be considered the general case, certainly not with good equipment. I'd suggest to try some ABX tests with  44.1 KHz data vs. 88.2 or 96 KHz resampled data (SSRC, CoolEdit, others?) to see if this happens with anyone's setup. I'd say that I can't hear a difference, but, to be honest, I haven't tried seriously yet.

As for true 24/96 signals sounding better than 16/44.1 ones, anyone can try http://www.pcabx-pro.com/technical/sample_...rates/index.htm

Oversampling Better?

Reply #36 –
I think that there is no need to ABX. Descending tones are characteristic of resampling. It doesn't mean that the DAC works better at 96 kHz, it means that it doesn't really operate at 44.1 kHz, there is something tampered with. The most probable is that the DAC is in fact 96 kHz fixed, and when a 44.1 kHz frequency is set, a sample rate converter processes all the data from 44.1 to 96 kHz.

There is no descending tone at all in the sweep when it is really played at 44.1 kHz. A treble tone is rising, and quickly disappears in complete silence. That's what is played in a pure 44.1 kHz converter, like in a CD player. I've just checked with the Marian Marc 2 soundcard (advertised for digital in/out without dither nor resampling), digital out, the DAT deck outside detects properly a 44.1 kHz SPDIF incoming stream. As an example, the SPDIF output of the SB live is detected at 48 kHz no matter what.

Given this, you certainly have a better sound at 96 kHz. The point is that you should get as good a sound burning the files on CD, and playing them in a CD player, at 44.1 kHz.

Oversampling Better?

Reply #37 –
Hmmm... some people have mentioned the fact that Nyquist proved that sampling at Fmax*2 is "enough". Well, I disagree. Being just a senior in Electrical Engineering Technology I can't really disprove the guy, and I am sure in theory he is correct.

In practice tho, I think he is not. Two examples. One is the digitizing scopes we use in lab. At the high end of the frequency range (I think 500MHz for the one's I am using this semester) they are taking 2Gsamples per second. That is 4x the max freq. I asked my professor why, if Nyquist blah blah and he said that for all practical purposes you NEED 4X to get an accurate representation. I mean, real world systems.

Another one is that in my digital class, we had a really simple A/D and a D/A system. We put in a sine wave in on one side, goes thru the A/D, into a shifter, thru a serial cable, into another shifter and out the D/A. Anyway, don't remember at what frequency we were running, but the output was distorted way before we got to the 2X spot.

So I really think that sampling at 96kHz is a great idea. But then again, I can't HEAR any artifacts or anything related to sampling at 44.1. Who knows... just wanted to share

Oversampling Better?

Reply #38 –
Thanks LoKi128,

So I'm not dreaming...

Oversampling Better?

Reply #39 –
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That is 4x the max freq. I asked my professor why, if Nyquist blah blah and he said that for all practical purposes you NEED 4X to get an accurate representation. I mean, real world systems.

Maybe for getting an accurate *graphical* representation. But with the use of a reconstruction filter, which any proper DAC has, this is unnecesary, as Pio and others have explained for Nth time.

Hey, just do some tests with Cool Edit!! It is capable of drawing *perfectly* any 21 KHz waveform at 44.1 KHz, because it simulates graphically this reconstruction filter. (Edit: Well, it seems that Cool Edit is not so "perfect" at doing this... Anyway with a proper reconstruction filter, there's no need for higher sampling rates to properly reproduce high frequencies.)

But then, there's one difference between theory and real world, and is that, in practice, it is very difficult to have perfect response up to fs/2, that is up, to 22050 Hz in case of cd. But, there is no problem in getting nearly perfect response up to 20 KHz and even 21 KHz with today's DACs. Edit: With the use of external software upsamplers such as SSRC, you simply get closer to the ideal case (theory), instead of relying on the more "approximate" oversampling that all DACs perform nowadays. However, as 2bdecided says, this more ideal case has other effects  that can cause problems in real world, such as long ringing at the limit upper frequency.

Oversampling Better?

Reply #40 –
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So I'm not dreaming...

Nobody is saying you're dreaming. Again, if you hear descending tones playing the 44.1 KHz sweep, then there are obvious flaws in your DAC, because this doesn't happen on mine. Maybe it lacks a proper reconstrucion filter that filters at 22 KHz, I've seen this happens with my 96 KHz capable DVD player. In my case this causes high amplitude aliases over 22 KHz, that in you case could intermodulate with the original sweep tones, leading do descending products that fall into the audible range. Or maybe there is just some bad resampling-like process.

Oversampling Better?

Reply #41 –
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I think that there is no need to ABX.

I was refering to 96 KHz sounding better in general, not for this particular (obvious?) case.

Oversampling Better?

Reply #42 –
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problems in real world, such as long ringing at the limit upper frequency.

What kind of problems long ringing should cause ? Intermodulation ?

Oversampling Better?

Reply #43 –
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problems in real world, such as long ringing at the limit upper frequency.

What kind of problems long ringing should cause ? Intermodulation ?

Yes, but I guess it is a *possible* problem, depending mostly on the equipment. But I really don't know how important is it in practice. Maybe in some cases it is, maybe it is not most of the times. I have simulated the effect into Cool Edit Pro, and with some induced distortion and synthetic signals (impulses and sines) it is quite noticeable. But I haven't done any tests with real music and real equipment, so I don't know.