Time resolution of digital sampling

[PeterSt]

... and the one signal would heavily influence the other ...

[PeterSt]

So Manuel, what is your opinion about the general stance of many people that (up to severe) ringing is harmless ?

[PeterSt]

12 minutes ago, manueljenkin said:

If I want to simulate real world sound waves I am supposed to try with dynamically varying amplitude.

 

I use Dirac pulses to tune (make) my filters.

Obviously Dirac does not exist in real life, but it represents the highest transients. Upsample that 16x (which is what I do - 44.1 to 705.6) and it is no Dirac any more. It becomes a more realistic transient.

 

Not sure how this would bring you further, but for me it is the base.

[PeterSt]

30 minutes ago, SoundAndMotion said:

Nyquest

 

haha

[PeterSt]

No, you better don't. :-)

But I thought this one was special.

[PeterSt]

Hi Manuel,

 

38 minutes ago, manueljenkin said:

What I'm understanding is you are using Dirac to determine the equivalent of window function and then convolving it with a sinc (oversampling from 44.1 to 705.6).

 

Haha, no, not at all. My filters are based upon genuine interpolation and that doesn't ring a bit. 😊

I can change the filters gradually so they start ringing, but this is so less so that it can't be audible (in my opinion). It's even hardly visible (scope). Of course according to the Mansr article ringing isn't audible anyway, but then maybe he must first listen to a ringing filter in order to come to the conclusion that somewhere the theories are not correct (my measurements are at a real DAC output).

 

What I do with the Dirac pulses, them being a representative of the highest transient theoretically possible, is observing them so their shape (and height !) is not molested in a fashion I deem wrong.

 

If you are interested, you should make yourself a file with unevenly spread Dirac pulses in them and you will be able to see the filter behavior on them (but have some sort of analyzer of sufficient bit depth to observe correctly).

With proposed official filtering (like sinc) the pulses become nice sines (sinuses) with as much energy above zero as below zero (while the original pulse is above zero only). With the filtering which is able to deal with this properly (I only know of my own), the pulses stay exactly as they are in the file, HENCE there are your transients.

Obviously this bears a price, namely the price of the filter being leaky. Still it shows 0.00063% THD at 1KHz, might this tell you something (unfiltered Redbook 16/44.1 will show 0.04% regardless the performance of the D/A converter).

 

I am working for more than 10 years on "transients" as such (squeeze out the best of them) with each other year (or so) another big leap forwards. Of course all in the realm of the least THD.

Only this morning I described an other milestone regarding perceived speed (a next huge step for the better), I now managed with a new USB cable (never mind for now how the heck a USB cable can be involved).

The story is infinite because it requires attention from all angles imaginable in the system-chain as a whole (my speakers are 118dB Sensitive, to name a crazy "requirement").

 

Point is (my personal hobby-horse point), that music types like I show here contain such wild transients all over the place, and as long as it is a transient (and not a frequency) they just can be rendered. Not that people understand this, but I can show it easily.

 

Your "volume" subject would be the same as my Dirac pulse, if it only happens one time. Then you have the transient.

If you see me talking about synthesizers, their On/Off sound and how the more speedy system will show the synths much better, it is about synths indeed being able to shut off a sound at once, and start it at full level at once just the same. Put this in a sequence of the same Offs and Ons and you'd have a frequency of some sort, which a bandlimited system just can show. That this On/Off sound is within a frequency itself is another matter. Thus, I am talking about a frequency of e.g. 1KHz but within that, the volume level goes On and Off all the time, maybe 10000 times per second. It is this what can be unveiled. But that won't happen with a smearing filter ... (I can show that easily too).

 

Please notice that making this audible (in good fashion) requires a lot of your system. For example, the output stage of my DAC can do 2000V/us for slew rate (the D/A chips themselves do less, but alas). And this is one element in the chain only which requires to do somewhat more than we are used to.

But I am sure you already know that ...

 

Regards,

Peter

 

 

[PeterSt]

11 hours ago, manueljenkin said:

How can a hit have negative energy preceding and following it.

 

Manuel, we must be very careful with "thinking" theories only;

In the electrical world (or the electrical domain), there's also this swing. If you think about that in the end all is always sines, no matter how "straight up" you want to see it in theory. If you think about squares you already know that. Well, the Dirac pulse does not behave differently.

 

These are three Dirac pulses of 2V :

 

 

 

Unfiltered, this shows the spectral content up to 1MHz :

 

 

 

In more detail, up to 100KHz :

 

 

 

Or for the audio band (~ 5KHz) :

 

 

 

And just the one pulse (time axis is in us) :

 

 

Of course you see Gibbs, but you also see the swing-up.

And down for that matter (a sheer ~200mV on the total of 2V) :

 

 

 

And more zoomed in :

 

 

Mind you, this too (above) is the going down from 2V to 0V. So the going down implies the swing up first. And if you look closely at the last part of the Gibbs effect, you see that the swing up which electrically is just there, again implies a small swing down first :

 

 

And if we would zoom in even further on the Gibbs effect, we'd see the same happening for each of the above "sines". And notice for your fun that the above does not show even (while in practice it will be) because this analyzer has its (band)limits too. 😞 So it looks like a 20KHz not decently low passed signal now (while it is something like 14MHz - analyser is 20Msps).

 

So ...

So before we forget, we were not looking at a frequency; we were looking at pulses with silence in between them. In itself such a pulse implies the most severe sh*t because its frequency is infinite (because the steepness is infinite). Nothing strange.

Now we are going to filter this nicely, and then this comes from it (time scale is ms now):

 

 

... and our pulses with silence in between them (btw at a rate of 10KHz) was turned into a 10KHz sinus.

And so instead of the synth showing all the frequencies possible (think ticks with "distortion" and which just is so and which also would be so for our ears (limited to 20KHz) we now hear a tone of 10KHz which just was not meant to be at all. Also notice the Voltage drop and you could even assert that our pulse train of +2V now has become a sinus with DC offset.

 

To finish this off, this is how it can be done with filtering means more suitable for it (this is 16x upsampled):

 

 

but keep in mind that this is actually a silent part:

 

and the one between -0.7ms and -0.6ms is wider spaced for better filter testing (the sinc filter will choke on this).

 

From the above we could (try to) learn that the one-sample pulse could be broadened to 16 samples, therefore making its distortions less severe;

Of course in practice these pulses won't exist, but the up (and down) going transients for sure do (and indeed DC offset related as you mention) and they better go instantly with some way down distortion product than a wheeeeep because it's turned into a sinus of some frequency.

 

Nyquist et all is not wrong, but different approaches exist. Mine makes the time domain prevalent but has the frequency domain in mind. Shannon and friends approaches it the other way around.

The results of both are very different.

 

DDDAC would be fine, as long as it allows at least one upsampling step for testing (and I am not sure about that).

But speaking of Doede Douma, I already wanted to ask you whether you are Germany-schooled. It is my experience that in Germany they allow this thinking - special engineering coming from that.

 

Regards,

Peter

 

PS: I can't get rid of the picture below. It shouldn't be there.

 

[PeterSt]

2 hours ago, manueljenkin said:

the previous signal before the pause would be continuing a slow decay and the new signal after pause will start it's slow attack and they would likely intersect each other (instead of being separated by pauses). If I try have the low pass at a higher frequency (which would also call for higher sampling frequency) I could "reduce" this transient modulation/error since it would decay quicker and hence have a better idea of the pause.

 

All correct. Here you see two of those pulses too close by or too low-fate sampled running into each other:

 

 

or viewed at the higher level:

 

 

... and this with the notice that this only happens because of the filter not being capable.

 

Please see through the fact that the 10KHz I used (thus 10000 time per second a 1-sample pulse) will not be a coincidence for the 44.1KHz original signal. This just allows sufficient spacing (silence) to not let run the samples into each other when we observe the necessary electrical ringing. It kind of means that the scratching DJ or ambient music creator (scratching is a/o these vinyl like ticks) is allowed to apply his text signals (my wife calls this type of music test signal (non-)music) has to take into account that he shouldn't apply more than 10000 of these On/Offs per second or else it can't be rendered at all by any means. In reality such a tick will be an as instant as possible transient which lasts maybe 10ms (implying DC Offset). Thus not one sample long, but 441 or so. Also keep in mind that synths can do such things on command, and that the artist must know a couple of things about audio too (but he can listen in real time at practicing / designing his track).

 

It could be important that I have a couple of these:

with a 3rd in the background you can't see and which I built myself (one year of soldering).

 

3 hours ago, manueljenkin said:

I would like to go through engineering books from German universities

 

 Nah, I don't think this stuff will be in books. But would you graduate there and come up with a thesis like you might have at hand, they would allow you to explore it because they seem not to be as strict and won't call you foolish to begin with. Open minded, that is.

 

3 hours ago, manueljenkin said:

But my question is, how do you predict where the pause is supposed to be on a pre sampled band limited music content?

 

Although my filtering is named Arc Prediction, it doesn't need to predict the placement of the (new) samples because remember, it genuinely interpolates. All what happens is that around the original sample (in our case the Dirac Pulse) a predicted path towards the sample emerges as well as a  predicted path after the sample. The original sample can be seen as sitting in the middle.

 

 

But don't be confused by this one above;

You can nicely count 16 samples on each side. This is because for Voltage we had one "going up" (obviously the left part) and one "going down".

And because this is measured at the output of a DAC (705.6 = 16x capable) this is not theory but practice. It is just the signal coming out - and ADC captured by a 20MHz sampler. Therefore the "swinging" is nicely visible too (mind the way smaller steps than the 705.6 sampling, let alone the 44.1 which already is not related any more ... it is just electrical behavior (subject of my previous post). And *that* pre- and post "ringing" also is not allowed to run into the previous (yep) or next sample (these side-lobes are *not* part of the filtering !). So this is how the slew rate comes into play.

Btw, this was taken from a version of the NOS1 DAC with way lesser slew rate than today's incarnation, and the plots show that the rise time to 2V is 90ns and the fall time is 160ns.

And also notice that because this is not a frequency but a single pulse only, there's also extra constraints on the fall time, because there's nothing drawing it to -2V. It just has to fall ... (which is why the fall time is slower in this case). 

 

As you can see we ended up in "DAC design" in a fashion which may people let scratch their head. But mind you, this is all design nobody is taught to begin with, because why need it anyway as a transient implies 14MHz of required bandwidth (we kind of saw that in the previous post).

 

[PeterSt]

23 hours ago, manueljenkin said:

I still use fft tools to check what has been done in the songs I'm playing and as a safety warning.

 

For me this has been mandatory;

I think for 3 or 4 months in a row I have been observing real-time FFTs from the music playing in this room. I now know quite well which instrument implies what and know for example the importance of the "roll" of a kick drum into quite infinite low frequency (but under 20Hz at least). But then we created speakers which went straight to 19Hz (+/- 0.5dB) or if you want by more normal measure, to 17Hz +/- 3dB) and all this speaker had to do was representing the kick drum real-life, with a previous speaker only lacking thee feel (the punch) in the stomach.

Easy ? not at all, because I tuned the speaker for "inaudible" THD at the low end.

 

In the end it is again the same thing: the low end has transients too which if possible are even more difficult to represent through loudspeakers (and all preceding those). So don't start with capacitors in the path ...

Don't start with bass ports either. Or boxes around the drivers (that implying another plethora of difficulty).

 

 

[PeterSt]

Maybe for now a last one:

 

15 hours ago, manueljenkin said:

I retained my doubts on dc offsets (variable)

 

First of all, quite some "music" exists which deliberately plays with some DC Offset (200-300mV). Actually I don't know nor wondered the importance of that when normal filtering would be applied (it may not understand it). Somehow I encounter this in, say, psychedelic music types, me not even knowing what it would do (make me hallucinate ?).

But I go further ...

 

Within the Playback software, I created the option to play with positive DC Offset.

The NOS1 DAC shows in real time the DC Offset on meters for it.

So yes, about (crazy) systems ...

 

I figured that the non-linear behavior of anything "amp" (even D/A) would turn for the better when only positive voltage would be used. Today I forgot all the arguments I could think of back at the time, but for quite some years people really played with that (they had to check for DC Offset at the output of their power amps during test-play, because I wouldn't allow DC Offset to the speakers (they won't sufficiently cool)).

On a side note, this part of the software is quite complex because of the starts and stops and the explicit feeding of a DC signal (thus all implied by software) like +1V. Skip a controlled stop and a BANG would be your share.

This latter requires the opposite of a fast transient. 😁

 

Manuel, this could be the lead-in to what you actually think of when mentioning DC offset.

All I can imagine is that indeed it will be so that when a kick drum has its hit, the roll I talked about implies relatively severe DC offset for the complete signal of that moment. Then it decays, lowering the DC offset.

So Yes, our "transform" must be able to deal with this (don't throw it out) but I have no experience with negatives around this phenomenon. And I always like to learn ...

 

On another note, even a low frequency (like 27Hz) is actually DC offset, but it slowly varies all the time.

And oh, new to some might be that while a DAC seems to work with A/C, internally it really is DC all the time. OK, for a PCM DAC this is so ...

 

[PeterSt]

A bit of a more quick response :

 

1 hour ago, manueljenkin said:

Does your Dirac interpolation take into consideration the possibility of inter-sample peaks?

 

Although there is no phenomenon like "Dirac Interpolation" (Dirac pulses are just used by me manually) to tune the filter settings), inter-sample peaks can't spoil the party really;

 

Of course, when a native 16/44.1 shows a sample near the digital maximum and Arc Prediction would go beyond 32768 (-32767) this is dealt with (the value is cut). But without looking into it at this moment, I recall that this would be a very rare situation because adjacent samples would already show the real maximum. It will look a bit like this (unfiltered data):

 

 

Of course this is not music (I think this is a again a 10KHz signal), but the headroom given by the mastering engineer will be depicted by the first highest peak you see here. The next sample at the positive side, which is quite lower, will extend, but never to higher than this high peak we see as this first highest peak. Again, this counts for the periodic signal and with music the chance will surely exist.

 

Please keep in mind that such a means is never perfect for the frequency domain and that no sample moves to an

1 hour ago, manueljenkin said:

https://www.hindawi.com/journals/isrn/2012/643563/ (lol I'm thinking crazier than you I guess 😜).

other place. This will mean that those peaks which need extension (which happens in the upsampling process), will actually form a higher average output level (because existing peaks will never shrink, unlike with normal filtering (where I think the total energy remains the same).

 

I looked into that for a few seconds for now, but at (very) first glance it looks like a kind of resampling thing. Or maybe not - not sure. Anyway, some kind of resampling has always been on my mind (5 years or so ago I started working on it, but it lays unfinished). 

[PeterSt]

@jabbr, Jonathan, think of a random (complex) wave form which can be made subject to PWM. Give it a 50% duty cycle and the sound is "off" half of the time. Any duty cycle can be applied. Also, any "depth" can be applied (the wave may not drop back to a complete zero V).

 

True, "each going back to the normal level" implies infinite frequency if the code of the synth makes the transient as how we could to it ourselves with a test signal, but the point is: that infinite rise can just be captured by analogue means (I mean, the D/A process can do it, as I showed it).

 

Maybe more simplified:

Suppose I have a normal song of a couple of minutes; now each other second I silence (manipulate the file) one sample (16/44.1). Would we readily hear that ? I don't think so. Would a real time FFT show it ? Yes.

Next I silence one sample 2 times per second. Then 10 times. And so on.

 

The story about frequencies and Shannon et all won't apply, I think. But *first* apply a reconstruction like I do it. Apply a sinc filter and you probably won't see a thing of it in that real time FFT. At least not in that once per second silence of one sample (it will me smeared out of the way).

 

I am pretty sure that wave forms of a synth can be composed of PWM like modulation.

I am 100% sure that my "ambient" type and other types (hip-hop) of music applies it the other way around - inject the vinyl like ticks. Often a few per second randomized (e.g. De La Soul), most often more "scratch like" (a train of such pulses).

All what's frequency in it, is the on/off rate, and further the technical sinus frequency of the steep rise and drop. Filter out the latter, and it's just gone (re-appears in your pro-rock flute which now behaves as a sax - haha).

 

 

 

 

 

[PeterSt]

So Jud, it seems that you were just one sample ahead of me.

hahaha

[PeterSt]

This was all a bit hard to follow for me. I may need more coffee first. A few small remarks though;

 

1 hour ago, manueljenkin said:

However the signal we capture has transients and it does have deviations from steady state. Also we don't have an ideal sinc low pass filter during our ADC.

 

I think this relates to this (for me) confusing correction:

 

1 hour ago, manueljenkin said:

2 hours ago, PeterSt said:

True, "each going back to the normal level" implies infinite frequency if the code of the synth makes the transient as how we could to it ourselves with a test signal, but the point is: that infinite rise can just be captured by analogue means (I mean, the D/A process can do it, as I showed it).

I suppose I can correct this sentence for you.

 

You can't include any ADC here, because already there the filtering will have been applied. This is how I said "how we could do it ourselves" because music won't do it - hence, create a test signal which would be illegal for music, UNLESS ... the music comes from a synth which didn't go through DAWs etc.

So to be clear: there is nothing in my mind which thinks that any transient from e.g. a castagnette, could be improved by another means of reconstruction. It is only about synthesizers with direct transfer to the audio file.

This should not be confused with a SDM means of (D/A) reproduction which might add another step of "smear". I mean, without discussing this separately, it requires a genuine PCM DAC (as in R2R) in the first place and without any filtering means (the good old NOS/Filterless). ... Which is obviously what I use very explicitly. ... Envision that right along with the design of the DAC, the reconstruction means emerged, that to be executed in-PC so it would be manageable easily.

 

FWIW, do not forget that per reconstruction, which always comprises of upsampling, the whatever spaces go smaller. Per my means this is just like that. With an averaging kind of means (sinc) no space will remain right from the start (the original level will remain, apart from one bit value or so).

 

Something else:

Somewhere the 10us emerged, possibly from my own plots, which were analogue captures as seen through a 20Msps ADC. Silencing one sample would imply a silence of 22us if you'd ask me (44.1KHz). This will never ever remain silent after even one step of upsampling (the silent sample will have broadened to 3 samples).

So this should not be confused with the one sample of (Dirac) pulse, which occurs 10000 times per second, in my example. This gives "infinite" space* for letting the pulse remain, as long as the original has space around it for the sampling rate of the time (44.1Khz). Notice that at the broadening of the pulse, the sampling rate increases with it.

*): I feel I am wrong at this and that the width grows faster than the sampling rate increase. But it is not important.

[PeterSt]

Jonathan, I really wonder weather you're reading all the posts. 🤪

 

8 hours ago, jabbr said:

 

In the case of a "missing sample", this isn't a sampled signal anymore, the digitized signal has been digitally modified.

 

This testifies of a Not, IMHO. The whole thing is about how synthesizers operate, were it about real-life examples. And this is not about real-life sampling. Haha.

It is explicitly NOT about a sampled signal hence no ADC is in order.

OK ?

 

The deeper subject at hand is not about Shannon/Nyquist being right or wong; it is about when it exactly applies and when it can't (and not even when it shouldn't - in all your given poses it should !).

 

Quote

So let's stick to signals that have been properly digitized...

 

So we already did.

However, we were talking about how such a thing as On/Off would look like. Now I could make you a file from one of my synths, but we can also manipulate an existing file in the same fashion (this is a controlled virtual test).

 

[PeterSt]

8 hours ago, jabbr said:

 

You can't maintain that the impulse isn't sharp enough and also maintain that your hearing is bandwidth limited. The only way you can sharpen the impulse is by adding back higher frequency harmonics.

 

Let's not care about our bandwidth limited hearing (I started that myself). Let's care about your explanation of the plots I showed (again, it looks like you never saw them).

What we perceive of what I showed is an other matter for now.

[PeterSt]

6 hours ago, manueljenkin said:

For steady state sinusoids you can reliably estimate the frequency once you have atleast the minimum required samples and either align the sampling points properly or have proper window functions.

 

Very well said !

And this is not in order here. It can't because it isn't there. There is no frequency at hand ...

 

STILL it is so that for the pulse to rise in 90 degree fahsion, an unlimited frequency is required. Nobody in this thread doubts this. And worse, because it can't exist, the steepness won't be 90 degrees but less. So no matter digital (PCM !) could imply it (and synths can really do that), in pratice that will imply distortion (formally that would be correct) because the real world is not able to do it.

Although this is not really the subject, from this follows that any means that would be able to create such samples in a file, should obey the physical (slew rate !) limits on the system it's imposed to. If not, we'll have garbage.

[PeterSt]

 

 

 

 

This would be the limit of the NOS1a (G3 is way better) on its own. Something like 50ns and 160ns respectively. Make the spacing of transients smaller, and the garbage will be your share.

And of course, filtering this out also helps sufficiently, but hey ... (see underlying subject).

 

This is a DAC. But what about the amps ? the speakers ???

So True, for various reasons the spacing of transients need to be sufficiently large in order not to mess with the system's capabilities somewhere. It will really be ugly otherwise. And that it *is* ugly to begin with (with everyone's system) is easy to prove by means of over and over again making things faster which helps hugely. That I seem to be the only one working on such project ... too bad actually, because I am slow on my own.

 

 

 

[PeterSt]

22 minutes ago, jabbr said:

In the case of a synthesized series of samples, it is what it is. It’s not directly analogous to a recorded series of samples because the sequence isn’t bandwidth limited. 

 

Right.

As long as we remember that your preferred filter *is*.

(but mine may not be 😁)

 

23 minutes ago, jabbr said:

Typically a “missing” sample is an impulse, which sounds like a click. The amplitude depends on the width. But of course in a synthesized sequence, there is nothing “in between” samples.

 

Hmm. A missing sample is just that, and its amplitude is as deep (!) as the amplitude of the adjacent (non-missing) samples.

 

Why do I have the idea that you are working with a theoretical pile of data, while I talk about music data a.o. comprising of synthesizers ? You know, the Korgs and Yamahas and Rhodes and such.

 

28 minutes ago, jabbr said:

but if you want to know what it looks like you can look at the output of your software.

 

Do I ? ... I think I just spent a dozen of posts showing that ?

OK, you want more of that. Here:

 

 

Or up to 450 KHz:

 

 

And as a bonus in-band:

 

 

Surprised ?

Anyway, is this super-sh*t (as in hash) or could this be just what we want ?

Let's keep in mind that this started out as an infinitely steep rise (infinite frequency). We made the rise slower / less steep. Still many frequencies remain. Enough to perceive that "tick" (or transient in general).

And most certainly no 10KHz whine with DC Offset on top of it.

 

... But I didn't say I was finished. 😏

 

You know what this is ?:

 

 

No, it is not the same plot as before. Look in the right-hand side. This is sinc filtered ...

Ah. Oh. Eh ?

 

This picture I showed already earlier in the thread:

 

 

It belongs to the FFT from the previous plot. A sine.

While this is what it should be:

 

 

Keep in mind that all what you see is measured at the output of the DAC. There's no theories anywhere.

It is true that this comes from manually created data, that representing the worst transients that could happen in music files (and still only coming from Klaus Schulze et al). And all we'd want is preserving these transients as much as possible, without sacrificing the frequency domain too much (low distortion).

 

Peter

 

 

 

 

[PeterSt]

4 minutes ago, jabbr said:

 

  On 2/20/2020 at 3:15 PM, manueljenkin said:

Quote

 

  On 2/20/2020 at 9:15 AM, manueljenkin said:

... science studies do show humans can discern a time precision way above what a 48khz sampling rate can reliably capture (5micro seconds is what I remember, check some MIT studies and stuff).

 

 

At least something is wrong there.

I mean, you did not quote from Manuel (not your fault, I'm sure).

[PeterSt]

7 minutes ago, jabbr said:

This is how the thread originated.

 

However, it is Manuel where I started responding to. And he (virtually) responded late to something Jud said, who responded to Archimago, who quoted form Mansr's work.

 

As many threads this one went in a different direction than the OP intended (although it remains related).

 

I don't see the problem ... (apart from you consistently working with your own subject (which indeed could be the OP's subject).

It could be better to stick with the current subject instead of nobody understanding why you are so persistent in talking "frequency" while no frequency is in order since Sept. 20.

haha

[PeterSt]

12 minutes ago, jabbr said:

Alternatively the "scientific studies" may not exist or be wrong.

 

About that and mere to the OP's subject - maybe. Or let me put it differently (could be interesting):

 

Where you persistently talk about

a. a steep rise implying a high frequency in the file (my translation of your words)

b. while we are able to perceive a transient and THUS will be able to perceive a high frequency (like 30KHz) (your own words)

...

this is all putting on the wrong foot because nobody says or claims that.

Do you never perceive the vinyl-like ticks ? ah, probably not, because you listen through a sinc filter.

Would you look in the file for this, you will not find a frequency. Why ? because it just is not. A transient is sufficient to do it. A tick. Probably with some DC offset beyond it (to make it better audible).

 

The studies won't be wrong. But they skip this phenomenon (maybe not strange if it is so difficult to bring it across; sadly my English does not help with this - sorry about that).

 

[PeterSt]

Apologies - I only now see (and remember again) that this all sprung from Manuel indeed. But Don Hills made it a topic. OK.

 

Something else, for fun and maybe offtopic but not sure:

 

How can it be that I showed the Gibbs phenomenon at (IIRC) 14MHz, measured from the output from my DAC ?

Mind you please, this was from a MHz sampler (ADC) thus not fully legal (which the plot shows and which I mentioned). Now ...

 

1/14,000,000 = 0,000-000-071-42x

71ns.

 

Can we hear that (it *is* a frequency this time) ? No.

Not sure where the math in the OP (from Don) originates, but 71ns is what I would say. Just because my DAC shows that, and which is the result of a transient which originally requires infinite frequency to do its job (but which transient I flattened 16x).

It is electrical behavior which I think can be calculated with math (Voltage jump is +2V, but the one sample turned into 33 samples).

FWIW, have fun. But let's notice that when we'd upsample 8x instead of 16x, this ("Gibbs") frequency will change. The amplitude of it also will change. So apparently the sampling rate can imply a resolution (better : an implied frequency) and to me it seems that the lower the sampling rate, the higher this frequency (I did not check this), if only the transient remains the same. Something like : the less the sampling is suitable to catch the transient (in digital) the more the amplitude and frequency of Gibbs will be.

What to do with this ? nothing. 

[PeterSt]

15 minutes ago, manueljenkin said:

Studies exist: http://boson.physics.sc.edu/~kunchur//Acoustics-papers.htm .

 

Oh, but Mr Kunchur is also into cables. Now nobody will believe him.

Anyway, wow.

[PeterSt]

2 hours ago, manueljenkin said:

It doesn't even need to be a square, you can even have a 5khz sinusoid begining after say 5s, apply a sinc low pass, at say, 20khz and see the behavior around this 5s instance. Transient is a change of state, a change of flow

 

A bit of something else (with same underlying subject):

 

 

The normal filter only fully develops after in this case 63 samples (filter length). Thus where the original frequency has an immediate start (apart from the electrical pre-ringing), the filtered sound is sluggish.

And this has nothing to do now with the transients we talked about so far ...

Or has it ? Music is full with starts and stops of everything. Even flutes (sinus instrument) have a start.