Time resolution of digital sampling

55 minutes ago, SoundAndMotion said:

My problem is that you deny or ignore facts that are inconvenient for you, or you don't understand them. 

Well I think that can be flipped back to you too! If you were really open about this and were really trying to help me, you should have

 

1. Acknowledged that the equations described in man's post relates only to steady state condition and transient condition is different. The extent of deviation, we can work out after that and how much it relates or not. But you refused to. Either you didn't know that earlier, or if you knew you had actively tried to hide that away (which is the opposite of helping).

 

2. Given me enough indexes and relatable paper links to show me how much is a real world transient scenario, and what kind of wave shape it exhibits. Then we could really work out how things move on.

 

3. Not try to actively dilute or inhibit exploration. You probably have explored something and come to a conclusion, but it's not set in stone and you never published your findings. Let someone else explore, you may have missed things. You're trying to blindfold someone from exploring. Maybe you could spell out how you came into the conclusion then I could see where I can reduce attention at.

 

4. I can be stuck on transients because someone started the post saying I am blatantly wrong or misinformed. Nope I'm not. Transient scenario is the proof.

 

Yes all those rhetorical questions have been in my mind even before you asked me. But I don't really have the right apparatus to measure and come to a conclusion on the exact numbers. I do know my way around math and I engineering so I do know how to correlate between real world vs ideal number games. I have also had a fair share of experience in audio processing and psychoacoustics. I just use fft to check if my music has been horribly high passed/low passed or band passed. Maybe a few idea about the instruments in the place.

 

I certainly think you're trying to help me but there's also a part of you which wants to stop me from exploring. It definitely isn't the horrible thing what I experienced from at that one corner headfi, people often showcasing personal opinions as facts, and actively trying to bully/harass in other threads. You are not one of them, you're a much nicer person. But stop trying to inhibit someone from exploring because you have an opinion of it. You're welcome to share how you came to your conclusion, I can use it as reference.

5 hours ago, PeterSt said:

 

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.

Hi Peter,

 

I went through the Dirac topic. 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). I believe you are adaptively changing the window period and height depending upon the samples and tuning it to be done through an algorithm. You're adaptively changing the window function to change the pre/post ring properties at that particular sample instant. Am I right?

 

Thanks and Regards,

Manuel Jenkin.

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

 

 

14 minutes ago, PeterSt said:

Hi Manuel,

 

 

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

 

 

Hi Peter,

 

Thanks a lot. I can totally get what you're meaning, though I don't know the exact model you have that can achieve that low of a thd (and low spectral leakage) while still preserving transients.

 

I've had this doubts often about the Nyquist Shannon sampling, especially the low passing in ADC stage, exactly in the negative energy part for an impulse. How can a hit have negative energy preceding and following it. But then I used to convince myself that we are constantly listening to compressions and rarefactions so it may just be the natural behavior of an audible signal and that the present is always dependent on past/future. I retained my doubts on dc offsets (variable), and non linearities in forward vs reverse motion, and of course uni directional impulses (which would just be a sudden hit, and only the decay would have ringing). All of these impart to deviations from normal sinusoidal behavior which is what Nyquist Shannon theorem is based on. They would need special treatment when analysing, likely as different volume impulses of their own and trying to predict the best fit. And I'm also able to get what you mean with respect to synths.

 

This particular recording was done completely on code : All that makes us human continues, BT (this binary universe). I hope to try this on a really high quality system someday.

 

I regret my inability to try the NOS1, but do you know of any sub 300$ dac that I can "experiment" with on these stuff. Dddac1794 was interesting to me and within my budgets.

Thinking in uniform compressions and rarefactions often pushed me back to sinusoid theory. But my doubts on validity of sinc low passing remianed, never understood how one could have a proper sinc based low pass in real world. Capacitors certainly don't behave that way. Now I got my answer. Thanks.

 

Also feel free to link me to your usb cable thread. I currently enjoy my uptone uspcb but I'm building a custom transport, and would like to know how leads on customizing my usb port design for audio performance.

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.

 

Hi Peter,

 

Thank you very much. I am not against Nyquist Shannon theorem. I am just stating people about the fallacy of taking what is valid in steady state and extending to transient and delay properties without required modifications - Gibbs phenomenon, Gabor limits, etc. Gabor limit was a particular tripping point of enlightenment for me.

 

I am not from Germany, neither was this in my course. But I'm glad to know that my understanding is fairly good. I would like to go through engineering books from German universities, in case they take this approach. I find it very precise and rewarding, instead of cutting off at an abstraction. Abstraction is easier when we start but it should not be treated conclusive when talks of precision come in. I learnt signal processing only through resources on internet, a few reference books and trying to derive things either on paper or intuitively. But I had courses on other parts of Electrical engineering in my uni so I was able to get in flow fairly quick.

 

Getting back to the topic. The overshoot and tiny ripples are a side effect of band limiting right? Now if I have a wider bandwidth I would likely have lower of these ripples is my understanding.

 

Now coming to the modulation of the timing delays that occur within intersample points. I can 100% get what you've done with your oversampler. And the false sinusoid being inserted in place of a time delay with a conventional Nyquist sinc filter. But my question is, how do you predict where the pause is supposed to be on a pre sampled band limited music content? We have chopped it already right - ie the sample itself is inconsistent and we can only "predict" which way it could have gone. It's easier here because you knew there was a pause as you were the one who designed the Dirac pulses. But how would you do it in a pre sampled music.

 

Another doubt about the whole factor of band limiting. When I want to evaluate steady state property of a signal, I can pass it through a perfect sinc low pass filter (above the signal frequency) as many times as I want and I wouldn't have any issues, the level would remain the same. But if I want to evaluate the transient property of the signal, every single attempt at low passing/band limiting would be smearing/modulating those points in the signal right?

 

So these timing delays, after band limiting, wouldn't exist as mere delays but rather a series of continuous signals different from the original form due to it being in the transient region - 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. I still think there will be scenarios where this false high frequency sinusoid will be added but I guess it'll be lesser than current scenario or be truly out of human hearing band for most scenarios (or would there be other modulations I'm not aware of yet).

 

Another issue I have with fft graphs is why do we only look at amplitude plots. Why not add phase plots. Sure they will be rotating, but that's what I really want to see and visualize. Spatial cues are highly related to phase. We can have a two different signals with sample amplitude vs frequency plot, with just the phase bring different right? Say 2 sines of 50 and 75hz, vs a sine of 50hz and a cosine of 75 hz maintaining same amplitude. Why do we stop the analysis with just visually homogenous signals.

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).

 

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).

 

 

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 ...

 

1 hour ago, PeterSt said:

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.

Thanks Peter, I would require a little more time trying to wrap my mind around the other numbers and content in this post, but I got on particular question in relation to this implementation. Does your Dirac interpolation take into consideration the possibility of inter-sample peaks? (Our sampling instant need not coincide with the peak position of the waveform, even after band limiting). I am confused because the images all show peak at the sample instant, but of course this is an impulse simulated at that particular point for visual.

 

1 hour ago, PeterSt said:

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).

Well bass is low frequency, not necessarily low frequency steady state sines only. It can be a low frequency square, triangle, or just a hit with the slew rate being visualized as low frequency dominant spectra. Of course transients help. That is what gives the <<slam>>. I'm actually headphone guy (shure srh940 is my favourite headphone + binaural or live recordings). But I do hope to get into speakers someday, of course diy following the principles you mentioned. Hard to do, but must be done, if fidelity was of paramount concern.

 

38 minutes ago, PeterSt said:

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 ...

 

This is a tricky part because it gets system dependant. When analysing a system, I believe we should analyse it's performance at each volume levels, and each polarity configuration because of the prescence of non linearities. We could extend it to each pattern/sequence of the above, but I guess that'll get too tiring, so maybe a subset like slew rate. Even a basic bjt in class a configuration would have different non linearity in +ve and -ve cycle due to early effect. Fluid movement has non linearities and it is unlikely the flowing air behaves the same way in forward action as it does in the other half of the cycle. Or maybe the addition of dc offset stabilizes something wrt magnetic interaction or something else, that's another way to look at it. We can't say for sure. With regards to transients, we run squarely back into Gabor limits hard. I would personally keep it as transients with its own envelope patterns, trying to decompose into dc + fft again gets futile because of the limitations involved. Dc would eventually be just an average, and yes as you increase the period of analysis the overall average value reduces because it is just an impulse.

 

We could also think of a paradigm shift with implementations like these : https://www.hindawi.com/journals/isrn/2012/643563/ (lol I'm thinking crazier than you I guess 😜).

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). 

I'm sorry for the naming issue (Dirac interpolation) 😅, I didn't know how to word it. Thank you for all your insights, I really had a nice learning session today. I got to confirm the inconsistencies I spotted, and also got to learn more.

 

That particular paper/article I linked is with respect to the ADC process - non uniform sampling and other techniques to be able to decipher out of band data. It is a paradigm shift from uniform sampling using Nyquist Shannon theorem implementations. Not much relating to oversampling or reconstruction directly, but rather about preserving the data in the sampling process in the first place.

 

I am going to take some time in exploring this entire area further. Got a lot more equations to write and solve.

@manueljenkin I'm glad you and @PeterStare exchanging ideas. And I'm glad you have some ideas to follow.

 

But I have to say:

On 9/26/2020 at 3:02 PM, manueljenkin said:

[snip]

3. Not try to actively dilute or inhibit exploration. .....[snip]

....You're trying to blindfold someone from exploring. ...[snip]

....but there's also a part of you which wants to stop me from exploring. ....[snip]

....But stop trying to inhibit someone from exploring because you have an opinion of it. ....

This is so far off the mark, I honestly have no idea what I wrote that leads to this. I'm offended. I would never hope to inhibit your (or anyone's) exploration. I believe our communication is pathological.

 

Good luck and have fun.

7 hours ago, SoundAndMotion said:

@manueljenkin I'm glad you and @PeterStare exchanging ideas. And I'm glad you have some ideas to follow.

 

But I have to say:

This is so far off the mark, I honestly have no idea what I wrote that leads to this. I'm offended. I would never hope to inhibit your (or anyone's) exploration. I believe our communication is pathological.

 

Good luck and have fun.

If saying this directly in your face felt offensive to you, you have started atleast 3 comments prior to this, always in a negative tone, and I have tried to be polite in all those instances. Maybe not directly, but passive aggressively the intent in those comments felt to be something directly targeted to dilute my argument. You've constantly said I am ignoring facts, or acting beyond bounds when I really am not. I'm not thinking out of the box, my box is just bigger. A personal article by one person (or troll) doesn't equate to a reference material for me. I don't really have time to trace back the fallacies/abstractions/holes assumed in these "debunking" articles. If you really want to debunk something, write it as a paper or journal, get it peer reviewed and publish it through aes/ieee or any other verifiable organization, then I'll have a look. Even that is not set in stone, science always evolves itself, but if something is wrong there, it is atleast worth trying to find and correct since it would likely be a reference to engineers/scientists. I am just paying attention to detail in areas you guys have ignored, not tracing something unscientific. Whatever i am saying is well within the bounds of mathematics.

 

I'm sorry if you didn't like the wording, but that's how I really felt, and I expressed it only after being constantly twisted with the content I was expressing. And even now you've cherry picked the sentences you want to argue upon ignoring the other points I've mentioned. You can read the full paragraph, I am open to your opinions provided you have put enough thoughts to figuring out the angles I've been thinking upon. I am indeed open to anyone's thoughts provided they have given enough attention to detail.

16 hours ago, manueljenkin said:

Does your Dirac interpolation take into consideration the possibility of inter-sample peaks? (Our sampling instant need not coincide with the peak position of the waveform, even after band limiting). I am confused because the images all show peak at the sample instant, but of course this is an impulse simulated at that particular point for visual.

 

Nyquist Theory works. That said its not unreasonable to sample at a higher frequency in case ultrasonics are important. Do you need to capture >100kHz? Then there is high bit rate SDM e.g. DSD512 recording -- enough?

15 minutes ago, jabbr said:

 

Nyquist Theory works. That said its not unreasonable to sample at a higher frequency in case ultrasonics are important. Do you need to capture >100kHz? Then there is high bit rate SDM e.g. DSD512 recording -- enough?

This was relating to the interpolation technique used by Peter. It is slightly deviated from normal nyquist based sinc filter, and for some good audible reason. Nyquist theorem covers inter sample peaks (provided bit depth headroom is there during reconstruction). The interest here is to reliably capture and reproduce "pauses" that are as quick as 10us, not necessarily sines with that period. Its not really ultrasonics but the representation can fall out of the 20Khz band limit.

 

DSD has other trade offs (you need to use up a portion of the higher frequency sampling to make up for the loss in bit depth), and its hard to represent a constant DC (we always get a wiggle moving up and down, though small in quantity) ; gets lesser in quantity on the audio band as we move to multi bit dsd or increase dsd sample rate, but to completely eliminate it, you'll again get a limit tends to infinity condition. Also I guess the noise shaper will still want a low pass somewhere so not free from transient issues, though the pass band be pushed up and up.

17 hours ago, manueljenkin said:

The interest here is to reliably capture and reproduce "pauses" that are as quick as 10us, not necessarily sines with that period. Its not really ultrasonics but the representation can fall out of the 20Khz band limit.

 

"pauses" of 10us are ultrasonics, no two ways about it. You simply can't say that you care about a 10us event without being interested in the frequencies that represent the event.

1. If it is audible should it still be called "ultrasonics"?

 

2. Frequency is something that is mainly referring to periodically repeating signals. A lot of sonic information is not repeating, quite an amount of them happen only once. We just typically extend our visualization using fft approximations for ease of analysis. This visualization depends on the wave structures that precede and follow them.

 

If I am hitting a constant scale say C in a flute or guitar I'll have a uniformly repeating pattern, and running fft will give me the full properties of the signal (assuming I'm hitting a perfect C constatly without distortions and my adc is also reliably correct). However when I start to play music, I am varying my "frequency/wave shape smoothly" and also the amplitude. We run into trade offs when visualizing just the fft plots obtained after windowing.

 

The 10us pause in Peter's example related to 10khz false sinusoid with Nyquist reconstruction because of the way the next few pulses were placed in that example. It can be different in other scenarios. Hard to predict it without looking at the preceding and succeeding samples. This is not like a continuous cycle of 10us pause, 50us sine, 10us pause, 50us sine. The real world occurence of these is not periodic or predictable (atleast for now, with a general Nyquist Shannon sampling at Redbook cd).

1. Saying ultrasonics is audible would be an oxymoron. Either change the definition of ultrasonics or coin a new term. Yep it's a semantic issue, but I think I have a reason to be pedantic about it.

 

2. Trying to decompose "everything" to frequency bins with amplitude levels is futile. Some scenarios (ones that get close to steady state sinusoid properties) approximate closer, others start to show erratic behavior depending on the scenario when it occurred when viewed as fft. The window function, windowing period, and even the start and end sync points of the windower will heavily influence the visualized frequency spectra in these scenarios (that is you don't have a single unique way to visualize these, atleast with the normal Nyquist Shannon based sampling and fft on it other than keeping them as a separate transient signal). Also to note that we seldom look at anything other than the amplitude bode plot of the fft, conveniently ignoring the phase plots and dc offsets. 10us pause is a 10us pause, I don't think it corresponds to any one particular frequency. Is it out of the band of 0-20khz (sines)? yes. But it doesn't correspond to any frequency of its own. Same goes for a transient hit.

22 minutes ago, manueljenkin said:

1. Saying ultrasonics is audible would be an oxymoron. Either change the definition of ultrasonics or coin a new term. Yep it's a semantic issue, but I think I have a reason to be pedantic about it.

 

2. Trying to decompose "everything" to frequency bins with amplitude levels is futile. Some scenarios (ones that get close to steady state sinusoid properties) approximate closer, others start to show erratic behavior depending on the scenario when it occurred when viewed as fft. The window function, windowing period, and even the start and end sync points of the windower will heavily influence the visualized frequency spectra in these scenarios (that is you don't have a single unique way to visualize these, atleast with the normal Nyquist Shannon based sampling and fft on it other than keeping them as a separate transient signal). Also to note that we seldom look at anything other than the amplitude bode plot of the fft, conveniently ignoring the phase plots and dc offsets. 10us pause is a 10us pause, I don't think it corresponds to any one particular frequency. Is it out of the band of 0-20khz (sines)? yes. But it doesn't correspond to any frequency of its own. Same goes for a transient hit.

 

If you want to be pedantic, understand the math. No need to simplify. If you had a 10us pulse on/off that's 50 kHz, plus a bunch of harmonics, so can you hear any combination of frequencies 50 kHz and up? How good is your hearing?

 

Does a pulse of 10 us sound different than a sine wave? In that case you are hearing higher order harmonics. Nice.

 

Do you get it?

One isolated instance of a 10us pause is different from a train of 10us separated ups and downs. I understand the math and I do know transients cannot be analysed the same way. Most of the math is considering steady state analysis for a train of repeating signals. If they don't repeat you enter a trade off depending upon the window methods, the widow sizes and overlaps. You don't need to hear higher order "harmonics" to hear a pause. It is just a pause.

I propose a simple experiment. All we need is Audacity or similar software and a method to compare two files that is blinded.

 

Compare two files, one with a steady tone, the other the same but with a single missing sample at 44.1kHz sample rate. As I understand it volume may need to be reasonably high.

 

Can you tell which file contains the missing sample?

@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).