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Topic: Ripping Vinyl 192khz 24bit Considerations (Read 58574 times) previous topic - next topic
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Ripping Vinyl 192khz 24bit Considerations

Reply #25 –
Quote from: Juha on
IIRC, I read long ago on some site that using high samplerate (192kHz) in recording improves the AD conversion quality at higher frequencies (inside Nyqvist range) because of there are more samples to present the analog data as digital then (i.e. how many samples represents lets say 12kHz tone if I have understood it correctly).

It wasn't this site - http://electronics.howstuffworks.com/analog-digital3.htm but, maybe this site supports what I tried to remember.


Juha


That's audiophile crap. 24/44.1 is more than enough to make needledrops.

Ripping Vinyl 192khz 24bit Considerations

Reply #26 –
Quote
It's very simple, really.

If the analog signal contains NO content above Nyquist, then it can be reproduced EXACTLY by sampling at 2x and then converting back to analog. End of story!

It's a common nonsense. In short, no, unless you have an infinite stream of samples.
Longer answer

Ripping Vinyl 192khz 24bit Considerations

Reply #27 –
This has been an interesting thread which has degenerated into the debate between "audiophile crap" vs. 44.1/16.....I wonder, is there a definitive be all and end all empirical study (or set of studies) that one can read to prove EITHER side?  Just a simple google search the other way and one can also find other zealots pitted against the "HA crap."  If there are no such studies for either side, then it is crap+crap (or maybe crap^2).

Ripping Vinyl 192khz 24bit Considerations

Reply #28 –
Quote from: _m²_ on
It's a common nonsense. In short, no, unless you have an infinite stream of samples.
Longer answer


I already explained that things look different in practice. If something is nonsense then the linked 'longer answer'.



@ron: http://www.aes.org/journal/online/JAES_V55/9/

A carefully controlled double-blind test with many experienced listeners showed no ability to hear any differences between formats.  The results were that 60 listeners over 554 trials couldn’t hear any differences between CD, SACD, and 96/24.

That's just one but an in depth search should yield a couple of such tests (the results usually are that no one could hear any differences).
"I hear it when I see it."

Ripping Vinyl 192khz 24bit Considerations

Reply #29 –
Quote
I already explained that things look different in practice. If something is nonsense then the linked 'longer answer'.

No, you stated that things are different. But anyway, I started writing the blog post before you did and when it was ready and I realized that there was some talk about it, I stopped for a while to think whether posting it here still makes sense and decided that it makes more sense than not doing so.
Now if you think what I wrote is nonsense, provide some arguments because such statements are useless w/out a stated basis.

Ripping Vinyl 192khz 24bit Considerations

Reply #30 –
@xnor

thanks for the links.....will read


I do find it very interesting the zeal with which both sides of the argument state their case.  Seems like there are numerous labels remastering to 96/24, perhaps the better master is all that is really causing the effect?

Ripping Vinyl 192khz 24bit Considerations

Reply #31 –
Quote from: _m²_ on
Now if you think what I wrote is nonsense, provide some arguments because such statements are useless w/out a stated basis.


"decoder doesn’t use Shannon-Nyquist algorithm to recreate it"
This is nonsense because Shannon deals with recreating analog signals; an audio decoder has nothing to do with this.

"music rarely consists on infinite repetitions of the same signal, and that’s what Shannon-Nyquist theorem requires to work"
Shannon doesn't require any repetitions and an infinite signal is only needed for exact reconstruction. It still works with finite signals but the result will be an approximation of the original which can be good enough for us not to be able to detect a difference.

The 3999.5 Hz wave cannot be reconstructed perfectly because you have to give the bandlimiting low pass filter some room (like I've explained in my initial post).
But it's questionable how this file was created and resampled in the first place..

The interpretation of the waveform doesn't make any sense to me, nor does the conclusion for reasons I just mentioned.
I'm sorry if all of this sounds harsh.. and also for off-topic.


edit:
Quote from: ron spencer on
I do find it very interesting the zeal with which both sides of the argument state their case.  Seems like there are numerous labels remastering to 96/24, perhaps the better master is all that is really causing the effect?

Discussions get heated when people can't control their emotions (I'm not referring to anyone in this thread).
You're right, the master dictates everything and a bad master will always sound worse pretty much regardless of the format. (I have seen that it's not uncommon in the industry to use different masters for CDs compared to 'high-quality' downloads or SACDs for example. I was pretty shocked when I first saw this: the waveform of a 16/44.1 download and the 24/96 version of the same song looked very different. I don't know what they did exactly but at least the dynamic range and compression was different.)
"I hear it when I see it."

Ripping Vinyl 192khz 24bit Considerations

Reply #32 –
Quote from: xnor on
The 3999.5 Hz wave cannot be reconstructed perfectly because you have to give the bandlimiting low pass filter some room (like I've explained in my initial post).

Bingo!

"Now before I get to details, a remark: I never studied signalling theory"
Clearly.

Ripping Vinyl 192khz 24bit Considerations

Reply #33 –
Anybody who is seriously claiming that 16 bits is unequivocally sufficient for recording vinyl is nuts. By all means, record at 24 bits if you can: the benefits will at best be barely significant in a rare percentage of cases, but unless you are really crunched on space, the cost is basically zero.

I just measured the minimum spot noise margin of a raw 24-bit recording of a needledrop (vinyl background noise to the 16-bit TPDF floor). It's 13db. And I wasn't even trying very hard to find a quiet record, either.

Certainly recording at 24 bits is not a sufficiently big deal so as to care about rerecording something that was done at 16 bits, and certainly 16 bits is much more than adequate for the final product, and it may be true that I just have an unusually quiet setup (I do try). But "vinyl is far noisier than 16 bits" doth not a 13db noise margin support.

Ripping Vinyl 192khz 24bit Considerations

Reply #34 –
Man so many people came out of the wood work over this, so many different opinions.  I think I am going to have to just experiment and try everything

Ripping Vinyl 192khz 24bit Considerations

Reply #35 –
Quote from: pdq on
It's very simple, really.

If the analog signal contains NO content above Nyquist, then it can be reproduced EXACTLY by sampling at 2x and then converting back to analog. End of story!


That isn't what the theorem says.  You have to sample at greater than 2x.  At exactly 2x you will always sample at the same phase, but no information about what that phase is, so no information about the amplitude.  You might sample at the zero crossings and the signal will not appear to be there at all.


Ripping Vinyl 192khz 24bit Considerations

Reply #36 –
Quote
"music rarely consists on infinite repetitions of the same signal, and that’s what Shannon-Nyquist theorem requires to work"
Shannon doesn't require any repetitions and an infinite signal is only needed for exact reconstruction. It still works with finite signals but the result will be an approximation of the original which can be good enough for us not to be able to detect a difference.

Yep. That's the point of my post, reconstruction has to be imperfect. I think I made it clear I don't know how does it sound in practice.

Quote
The 3999.5 Hz wave cannot be reconstructed perfectly because you have to give the bandlimiting low pass filter some room (like I've explained in my initial post).

Are you trying to tell that if the stream was infinite it wouldn't work too? I'm not 100% positive about it, but I think it would. And with long enough signals it could be decoded with arbitrary precision, but still it wouldn't be because decoders don't attempt to do it.
Quote
But it's questionable how this file was created and resampled in the first place..

Sure. You're free to repeat the experiment.

Ripping Vinyl 192khz 24bit Considerations

Reply #37 –
Quote from: _m²_ on
You're free to repeat the experiment.

Contrary to what you state, the file is not sampled at 8000 Hz; it's sampled at 44100.  Presumably what you have done is taken a 8k file and resampled it, badly. A resampler with better stop-band rejection would have left nothing audible in the output; a resampler with a higher cut-off frequency would have rendered the sine wave correctly.  As has been pointed out already, filters with such narrow stop bands as would be needed in this example are difficult to achieve in practice; however, they are unnecessary: no-one is claiming that 44.1k is good (in practice) for any signal <22.05k (or that 8k is good for anything <4k).  8k came about from telephony where the target upper frequency was around 3.3k, far below the 3.9995k you are trying to squeeze out of it here.

Ripping Vinyl 192khz 24bit Considerations

Reply #38 –
Quote
Contrary to what you state, the file is not sampled at 8000 Hz; it's sampled at 44100. Presumably what you have done is taken a 8k file and resampled it, badly. A resampler with better stop-band rejection would have left nothing audible in the output; a resampler with a higher cut-off frequency would have rendered the sine wave correctly. As has been pointed out already, filters with such narrow stop bands as would be needed in this example are difficult to achieve in practice; however, they are unnecessary: no-one is claiming that 44.1k is good (in practice) for any signal <22.05k (or that 8k is good for anything <4k). 8k came about from telephony where the target upper frequency was around 3.3k, far below the 3.9995k you are trying to squeeze out of it here.

Wow, thanks for pointing this out, it seems that Audacity has broken export.
Anyway, when I save the project instead, it saves the file correctly.
And, not surprisingly, it sounds the same.

Even 999.8 Hz is severely distorted, although admittedly that's purely about waveform preservation, just ABXed it and didn't hear the difference between 8000 and 48000.

Ripping Vinyl 192khz 24bit Considerations

Reply #39 –
Axon, I would like to understand your claim about your "minimum spot noise margin" measurement. Perhaps you would be willing to elucidate a little if it isn't something likely to be already obvious to everyone but me (or it hasn't already been covered between my reading earlier today and when I get back to post this).

I'm thinking you said you measured some noise from an LP surface at -85dBfs, but what is a "spot noise margin"? Is it over some very small duration? How is the measurement made? Is this in a system where the LP signal peaks can reach somewhere in the vicinity of 0dBfs or one that would need considerable analogue amplification to achieve 0dBfs?

My system is fixed gain. A few LP Orchestral recordings have almost reached 0dBfs peak but normalization to the amount of +6dB to +12dB for my finished product is very common.

The raw recordings generally measure about -52dBfs to -55dBfs average RMS on unmodulated grooves between tracks (regardless of maximum music peaks), occasionally much higher. A high pass filter at 30Hz, which I use on most recordings, generally lowers the between tracks floor to about -60dbFs to -62dBfs (before NR or other processing).

Since my system noise floor is about -80dBfs average RMS (-102dB for soundcard, -90dB for phono preamp), the above seems to me to be a fair value for actual LP background noise. No improvement would seem possible through a quieter system. While I do record in floating point format, for subsequent processing, nothing would seem to be lost from the LP by instead using a 16 bit format. Do you think I have a definite misunderstanding of the situation or that I am doing something wrong to get such higher noise measurements?

Basically, my experience suggest that -85dBfs from the disk surface is not possible, although this would of course depend on the cartridge output plus any analogue amplification between the cartridge and the soundcard. Using my setup, but lowering the phono preamp amplification factor enough to reach -85dBfs for the LP background noise seems like a poor reason for claiming that 16 bits is not adequate unless we are talking about something different from anythng I know about.

By the way, based on some of your other posts, I suspect you might find this of at least passing interest (most of us would have to take a pass -- on the cost).
http://www.celemony.com/cms/index.php?id=capstan

Regarding some earlier discussion of LP processing and Sound Forge: When the product was owned by Sonic Foundry, their Noise Reduction 2 plugin was a separate product. The facilities included with the editor were fairly primitive. After Sony bought the line, the NR 2 plugin was added to some versions of Sound Forge (at a lower total cost than purchasing the plugin alone).

Both the declicking and NR abilities of this product in batch processing mode are better than many other LP/tape restoration programs. It may fare less well compared to some of the really expensive packages, but if your version of Sound Forge has this plugin (or its processes integrated into the editor) you do have the means to getting good results from most LPs.

Ripping Vinyl 192khz 24bit Considerations

Reply #40 –
Quote from: xnor on
The 3999.5 Hz wave cannot be reconstructed perfectly because you have to give the bandlimiting low pass filter some room (like I've explained in my initial post).
You could quite easily reconstruct the 3999.5Hz waveform properly from 8000Hz sampled data using a decent filter. Proper brick wall filters are easy. Long, but easy.

They're not used because, in the actual audio systems in use, this phenomenon occurs at 22.05kHz, rather than 4kHz, and so is inaudible.

A more gentle filter doesn't have to let anything through that you don't want. It can simply start to cut off at a lower frequency, e.g. 20kHz.

There are loads and loads of threads about this. I can't believe we're re-hashing this topic!

Cheers,
David.

Ripping Vinyl 192khz 24bit Considerations

Reply #41 –
Quote from: _m²_ on
Wow, thanks for pointing this out, it seems that Audacity has broken export.
Anyway, when I save the project instead, it saves the file correctly.
And, not surprisingly, it sounds the same.

Even 999.8 Hz is severely distorted, although admittedly that's purely about waveform preservation, just ABXed it and didn't hear the difference between 8000 and 48000.


Audacity's export is not broken. You're just, well, wrong.

Do you have any *earthly* idea how pointless your test sample is? In order to cleanly reproduce at 3999.5hz sine at 8khz sampling rate, you need a reconstruction filter with a 0.5hz transition band. Translation: the filter must be at least TWO SECONDS LONG. In addition to being hideously inefficient, such a filter will also ring for 2s (1s preecho, 1s postecho). So it's really a "test" of the worst kind possible: in order to pass the test, a playback system has to be not only slow, but sound like ass too. And interpreting anything out of Audacity's waveform plots of this wav are precisely as meaningless, for precisely the same mathematical reasons.

To say that Shannon-Nyquist Theorem "requires" an infinite signal to work is equally as logical as saying "Computing 2+2 doesn't work, because I *know* the answer must be 5". The "theorem" doesn't really care whether you are dealing with bandlimited data, timelimited data, whatever. The general behavior of aliasing in the Fourier domain is utterly unambiguous, predictable, and easy to interpret, and Shannon-Nyquist is so easily derived from such principles that calling it a "theorem" really overstates the complexity of the proof. For bandlimited signals, there is precisely zero aliasing. For timelimited signals, of course there will be aliasing, but it will occur at predictable and controllable levels, which, of course, ADC engineers have firm control over.

Sorry, normally I'm at least slightly less short about topics like this, but I have zero patience for lazy CS grads who act like armchair signal processing engineers without bothering to understand the math. It's *really* not that hard.

Ripping Vinyl 192khz 24bit Considerations

Reply #42 –
Quote from: _m²_ on
It's a common nonsense. In short, no, unless you have an infinite stream of samples.
Longer answer
What you're seeing is beating between the wanted signal (3999.5Hz in this case), and the first image (4000.5Hz in this case). The reconstruction filter should remove all content above Nyquist, but isn't doing so.

Quote
Now this is just example of what can happen, purely artificial, obviously. But you can experience different sampling artifacts. And not only with frequencies close to the maximum, with lower ones the problem is just smaller.
Any "problems" you see with "lower ones" will be because of images - frequencies as far above Nyquist as the "lower one" is below it, which should be being filtered out by the reconstruction/resampling filter, but aren't.

There are two take home points from this:
1. you can use as good a reconstruction filter as you want - audacity is not the only software in the world
2. in CD sampled audio, even without a reconstruction filter, what you have is exactly what you want up 22.05kHz, and then a spectral mirror of the 0-22.05kHz content above 22.05kHz. If you don't filter it out, the waveform will look quite strange, but the part that your ears can actually hear is perfect - your ears are doing enough filtering to make it work just fine. The reason for putting the filtering in DACs is because lettings lots of ultrasonic junk through can upset some equipment downstream, and intermodulation distortion in amps and (even more) speakers can make it has an effect within the audible range again.


Back on topic: 16/44.1kHz is enough, but
1) if your sound card is poor and doesn't filter out content above ~20kHz properly when recording (i.e. you get aliasing), then you can record at a higher rate (e.g. 88.2, 96), and then downsample in software.
2) if you're hopelessly careless with your levels when recording, but you have a very good sound card, then 24-bits could just about have some tiny benefit. Note: with a poorer sound card, the bottom 8-bits or more of the "24-bit" signal is all noise: better to set the levels properly and record in 16-bits than set the levels too low and record in 24-bits in this case!
3) floating point (in some software) allows you to be careless with levels when processing too. Though goodness knows what kind of processing you'd have to do to make this relevant - far more EQ than I'd ever want to apply!

Hope this helps.

Cheers,
David.

Cheers,
David.

Ripping Vinyl 192khz 24bit Considerations

Reply #43 –
Quote from: xnor on
A vinyl record can contain frequencies of [some ultrasonic value, doesn't matter if it's right or consistent], probably even higher.

Based on what I've read here and elsewhere (anyone feel free to offer or point to contradictory info), and notwithstanding the rare occasions when someone reports seeing a faint line in the upper reaches of spectrograms made from vinyl ripped at a high sample rate, it seems to me that vinyl's ability to reproduce what are thought to be ultrasonic frequencies is only meaningful to the extent that 1. the source instruments produced audible (thus not really ultrasonic) harmonics that high, and 2. those harmonics were preserved, at an audible level and without getting buried in noise, by every piece of equipment and media used at every stage—from multitrack recording on through to supplying a stereo mix to the vinyl mastering house (something quite often done via ordinary audio CD-R), and then during vinyl mastering, previous playback (the highest-frequency content is said to diminish with each play of the vinyl), ripping, and the format conversion for storage. If you consider the frequency limitations of the typical pieces of equipment in those chains, you'll find it's virtually impossible to justify a sample rate greater than 44.1 kHz for ripping vinyl, other than the reason David mentions in the post above.

Ripping Vinyl 192khz 24bit Considerations

Reply #44 –
Quote from: Batman321 on
Quote from: Juha on
IIRC, I read long ago on some site that using high samplerate (192kHz) in recording improves the AD conversion quality at higher frequencies (inside Nyqvist range) because of there are more samples to present the analog data as digital then (i.e. how many samples represents lets say 12kHz tone if I have understood it correctly).

It wasn't this site - http://electronics.howstuffworks.com/analog-digital3.htm but, maybe this site supports what I tried to remember.

Juha


That's audiophile crap. 24/44.1 is more than enough to make needledrops.


It's so easy to throw out that kind of statements without argument ... can you (or anyone else here) explain why it's audiophile crap?

Juha

Ripping Vinyl 192khz 24bit Considerations

Reply #45 –
Quote from: AndyH-ha on
Axon, I would like to understand your claim about your "minimum spot noise margin" measurement. Perhaps you would be willing to elucidate a little if it isn't something likely to be already obvious to everyone but me (or it hasn't already been covered between my reading earlier today and when I get back to post this).

I don't have enough time to respond to this with the attention it deserves tonight but I'll try to give a bit more detail here.

Note, I am *exclusively* talking about recording bit depth here. If one assumes a 72db SNR for vinyl ref. +0db (reasonable? no?), assume +0db records at 0dbFS, but then add +12db of headroom for playing the loudest 12" singles, and perhaps another +3db for particularly egregious instances of inner groove distortion on used records, then you're already to -87dbFS. And -10db is right around the edge of audibility for narrowband noise differences, isn't it?

By "spot noise margin", I mean, find the quietest part of an LP, look at its power spectrum, then create a WAV containing 16-bit TPDF and look at its power spectrum, then looking at how close the two power spectra are. In other words, subtract the TPDF spectrum from the vinyl noise spectrum, resulting in the "margin" between the two. I use the term "spot" to indicate that this is a frequency-dependent quantity, and I call this "noise margin" rather than "SNR" because there really isn't a "signal" here, just two sources of noise that I want to compare. If the spectra are dominated by broadband noise (which they are) and the spectrum analysis parameters are held constant, then, I believe, such a relative measurement ought to be meaningful.

I suppose that in hindsight "spot noise factor" would be slightly more formal, but I'm not sure any more understandable. :F

I measured the 13db margin as being centered at ~1100hz, with a bandwidth of a couple hundred hz or so. IIRC it was probably under a bark. But the margin was 16db or less for a *much* wider bandwidth (like 5khz or so). The recording was (of course) flat eq, with the gain set up to record +0db at around -30dbFS, which gives me 6db of headroom IIRC for my torture tracks.

If you're evaluating noise/SNR on an RMS basis rather than a spot/spectral basis then you need to be a hell of a lot more aggressive about your lowpass filtering. Everybody knows that the SNR of vinyl below 30hz is a dirty dog, but it's still a dog at 200hz; IIRC on a lot of records it doesn't actually reach a local minimum until 500-2000hz. I highpassed my snipped of vinyl noise at 200hz.

Don't get me wrong -- I really don't think 16-bit dither would ever likely be audible in this context -- but I really do think that's a closer call than some might imagine.

Hopefully I'll have more time to reply tomorrow.

Ripping Vinyl 192khz 24bit Considerations

Reply #46 –
Quote
So it's really a "test" of the worst kind possible: in order to pass the test, a playback system has to be not only slow, but sound like ass too. And interpreting anything out of Audacity's waveform plots of this wav are precisely as meaningless, for precisely the same mathematical reasons.

That's about what I meant by saying that it's good that decoder's don't work this way.
Quote
To say that Shannon-Nyquist Theorem "requires" an infinite signal to work is equally as logical as saying "Computing 2+2 doesn't work, because I *know* the answer must be 5". The "theorem" doesn't really care whether you are dealing with bandlimited data, timelimited data, whatever. The general behavior of aliasing in the Fourier domain is utterly unambiguous, predictable, and easy to interpret, and Shannon-Nyquist is so easily derived from such principles that calling it a "theorem" really overstates the complexity of the proof. For bandlimited signals, there is precisely zero aliasing. For timelimited signals, of course there will be aliasing, but it will occur at predictable and controllable levels, which, of course, ADC engineers have firm control over.

Maybe I was not precise enough. By 'work' I meant 'be able to reconstruct the signal perfectly'. For any decoder there is a signal that's won't be restored perfectly. So no, it doesn't work and can't work and even Master Shannon can't change it.

Quote
What you're seeing is beating between the wanted signal (3999.5Hz in this case), and the first image (4000.5Hz in this case). The reconstruction filter should remove all content above Nyquist, but isn't doing so.

I don't get it. How should the waveform look after reconstruction filter?
Quote
1. you can use as good a reconstruction filter as you want - audacity is not the only software in the world

Actually I used foobar and VLC to run the wav. Any suggestions?
Quote
2. in CD sampled audio, even without a reconstruction filter, what you have is exactly what you want up 22.05kHz, and then a spectral mirror of the 0-22.05kHz content above 22.05kHz. If you don't filter it out, the waveform will look quite strange, but the part that your ears can actually hear is perfect - your ears are doing enough filtering to make it work just fine. The reason for putting the filtering in DACs is because lettings lots of ultrasonic junk through can upset some equipment downstream, and intermodulation distortion in amps and (even more) speakers can make it has an effect within the audible range again.

But the same is well visible on a waveform around 1/2, 1/3 so on up to 1/6 N too. And these are within human hearing range.
Now whether it's audible - 1/4 is not for me and I have no idea how about the others.

Thanks, 2Bdecided, you're helpful.

Ripping Vinyl 192khz 24bit Considerations

Reply #47 –
Quote from: Juha on
It's so easy to throw out that kind of statements without argument ... can you (or anyone else here) explain why it's audiophile crap?

Because audio reproduction at 44.1/16 is sufficient.  The public has an appetite for higher definition (e.g. TV) but if they can't perceive a difference, they don't buy it: 30+ years on and, despite trying (e.g. with formats such as DVD-A), no-one has been able to convince that 44.1/16 is lacking in any way.

Ripping Vinyl 192khz 24bit Considerations

Reply #48 –
Quote from: Juha on
Quote from: Batman321 on
Quote from: Juha on
IIRC, I read long ago on some site that using high samplerate (192kHz) in recording improves the AD conversion quality at higher frequencies (inside Nyqvist range) because of there are more samples to present the analog data as digital then (i.e. how many samples represents lets say 12kHz tone if I have understood it correctly).

It wasn't this site - http://electronics.howstuffworks.com/analog-digital3.htm but, maybe this site supports what I tried to remember.

Juha


That's audiophile crap. 24/44.1 is more than enough to make needledrops.


It's so easy to throw out that kind of statements without argument ... can you (or anyone else here) explain why it's audiophile crap?
Because it shows the sample points joined by straight lines, saying "When the DAC recreates the wave from these numbers, you get the blue line shown in the following figure:"

There's not a DAC in the world that joins the sample points with straight lines like that.

Cheers,
David.

Ripping Vinyl 192khz 24bit Considerations

Reply #49 –
Quote from: _m²_ on
But the same is well visible on a waveform around 1/2, 1/3 so on up to 1/6 N too. And these are within human hearing range.
Yes, the beating is visible in an unreconstructed waveform (i.e. sample points).

Let's use some numbers...

48kHz sampling (easier numbers, but sample principle applies at 44.1kHz, or any other value).

Nyquist = 24kHz.

Sample a 17kHz tone. Just looking at the sample points, it looks a little ragged. You're seeing the effects of sampling - you get images at higher frequencies. It's exactly what would come out of the DAC is you did no reconstruction filtering at all, but just set the output voltage equal to the sample value at each sampling instant - no interpolation or anything.

So 17kHz becomes 17kHz + 31kHz + 65kHz + 79kHz + ... (infinite series, in theory).

It's the extra 31kHz + 65kHz + 79kHz + ... which make the sample points look more ragged than the 17kHz you start with.

It's the 17kHz tone, and only the 17kHz tone, that you ear can hear (if you're quite young) - i.e. exactly what you started with. Nothing more, nothing less.

Hope this helps.

Now, click that FAQ button top left, and read some useful threads!

Cheers,
David.