Digital Show & Tell ("Monty" Montgomery @ xiph.org)

"Digital Show & Tell" is distributed under a Creative Commons Attribution-ShareAlike (BY-SA) license. Learn more here: creativecommons.org/licenses/...
This video was originally created by Christopher "Monty" Montgomery and xiph.org.
Original Video: xiph.org/video/vid2.shtml
Learn More: people.xiph.org/~xiphmont/dem...
00:00 - Introduction
03:36 - Stairsteps
08:40 - Bit Depth
11:35 - Dither
17:19 - Band Limitation & Timing
21:55 - Epilogue

[@leyasep5919]

Why is it not public ? It's such a gem !!!!

[@vuongnh0607l]

Probably because it's a reupload of someone else's video. There's a link to the original in the description box.

[@serenity1378]

@@vuongnh0607l It's creative commons, there's nothing about reuploading it that would cause issues or require it to be private.

[@giantnoah]

@@serenity1378 Yes but if it was posted publicly it might seem like he's taking credit for the video.

[@serenity1378]

@@giantnoah That's not how Creative Commons works. You literally just put the license and creator along with the material shared.

[@giantnoah]

@@serenity1378 I'm not talking in a legal sense, I'm sure you could upload the whole thing legally. I'm saying that if he posted it to his channel it might look to a viewer like he's taking credit.

[@daniel.s.stefanov]

Finally someone with a spectrograph and oscilloscope to make audiophiles cry over their 900$ platinum-plated USB cables 🤣

[@RAFMnBgaming]

Those guys are no way using something as pronouceable as usb.

[@lapub.]

Leave Britn, err, audiophiles alone ! They give me so many moments of bliss... with "The fuse direction" "The CD shaving" "The ethernet cable that allow bytes to flow at the right order"' and so many other things.... Only a thing is true SOME lp sounds better than CD, but only because CD mastering suffer of loudness war that lead SOME cd have less dynamic range recorded than the one engraved on the LP even played with the lowest end player, and sure this is a sad thing !

[@DobroPlayer12]

I remember when I first saw this amazing video 10 years ago being so disappointed that he hadn't made more videos

[@diegotz8]

I remember reading the article he mentions at the beginning back in the day and being blown away, thank you for uploading this!

[@Diego-Garcia]

Sometimes I think everyone can make good presentations... until a see people like Monty doing a presentation.

[@ThomasZander]

Can we please make this a mandatory training for everyone who spends money on hifi equipment?

[@petercook7502]

That comment makes no sense given tha conent in the video.

[@OrzoMondo]

There will always be someone who says "No way, 192 KHz is better, I can hear the difference!". These are the people who can "hear" the difference a $5k network cable makes. :) Thank you for this great video!

[@dirg3music]

I always think "no you can't mr Simpson, no one can". Lmao

[@Roger_Gadd]

Maybe thirty years ago there was a difference but now improved sampling accuracy and band limiting techniques negate any benefit of the higher sample rate.

[@graealex]

There is a general fallacy here. For example, audio mastering will usually employ higher bit depth and higher sampling rate. Which makes sense, for example if you want to change volume, i.e make something louder, you need more bits. Generally when manipulating any signal, having some headroom makes sense. That's equally true for images and video, where you want the RAW data for post production. "Audiophiles" then thought that because mastering uses "higher quality audio", that it would be beneficial to play back that exact audio quality. But unless you can somehow upgrade your ears, OR you plan on doing some heavy post-processing, it'll never make a difference.

[@daniel.s.stefanov]

That is sometimes true. However, I riddle you this - if you can hear the difference between two samples, how do you tell which is the "better" or "more correct" one? :) "The one with the higher number of stuff, obviously" isn't a valid answer :)

[@OrzoMondo]

@@daniel.s.stefanov very good point. Unless you can hear artifacts (like distortion), even a different frequency balance or "stage width" is not necessarily an indication of one being better than the other.

[@RannonSi]

I really enjoy Monty's presentation. What's he doing nowadays, approximately 11 years after?

[@gblargg]

Glad someone put this video back up. I hadn't been able to find it for years.

[@cancername]

I love Monty. He's an awesome presenter.

[@alib8396]

Wow, I'm in awe of the presentation itself. Very well made. it reminded me of watching those old films made by GM and Ford explaining some mechanical principle related to cars with props and cut open parts.

[@XDjUanZInHO]

The animations really show clearly how deceiving digital sampling can be, thank you for the demo!

[@christopherdunn317]

I don't think its deceiving, i think its just the way it is other than what people think in there own way !

[@XDjUanZInHO]

@@christopherdunn317 there's lots of pitfalls in the passage A/D and D/A, the one shown is just one of them. I mean, I do consider something to be deceiving if the act of looking into it doesn't necessarily reflects how the signal actually is, there's a possibility that you're signal never captures the maximum and minimum of the real waveform, just by occasion of your phase being just a bit more to the right than usual, and you'll *maybe* be able to detect it after looking into the frequency domain of the signal

[@JTheoryScience]

this is better then most youtube quality educational video by a huge margin

[@AvithOrtega]

I remember seeing this video 11 years ago, I noticed it was veery informative and helped me into understanding a lot about audio. And there is a lot more interesting info in their website, totally recommended!

[@Stevie_D]

Two words - EXCELLENT and INFORMATIVE! Thanks for posting that ... even though some of that was a replay from your last video, I replayed this one twice.

[@camdonhill]

Interesting. Thanks for posting!

[@yashvirmahdoo1587]

Thank you for this video, this has cleared out all the lies.

[@BlastingAgents]

What an awesome, on point, presentation.

[@gr18.n1k]

Super cool and inspirational content. I'm crazy glad youtube recommended me this channel!

[@wesleyboynton6535]

What an incredible presentation and what a smooth presenter.

[@jordankokocinski506]

Great video, thanks for sharing.

[@herzglass]

Very well made video! Love your overall style of presentation. Sharp. On point. Thanks a lot.

[@MOONBASE_Stereo_Side_Touchdown]

WOW ! Mind blowingly informative. cheers.

[@Lanchonito]

just perfect

[@matricasrpska]

Fantastic video and production! You condensed material from Digital Processing course that I had at university into 25 minute video.

[@irisharizona4187]

I need this man in my life.

[@mr88cet]

Really excellent illustrations! Thanks. The only place where I personally can imagine higher sample rates and greater bit depths mattering much is for mastering rather than distribution (i.e., mix-downs). More precisely, if you’re recording a bunch of tracks and manipulating them considerably - boosting their volume or applying EQ, round-off errors can accumulate. In analogy with video, if you’re creating an HD video, you’re wise to record the source assets in 4K Or at least conceptually speaking! So there’s your next video: How much value does, say 96KHz 24-but audio, have for source material that gets manipulated prior to mix-down?

[@Mix3dbyMark]

Awesome

[@Ioganstone]

What it is, followed by what it does, great stuff.

[@BandoLyrix]

People like this make Audio School important 🎉

[@korbensc7218]

Great Video.

[@naantipa]

This is a great video and demonstration. A minor quibble: pixels are in fact finite in area. They represent the accumulated number of photons that impinge upon a photodiode, which has a defined and finite active area, over a finite time. To be fair, it is never a true square, but it is certainly closer to square than it is to an infinitesimally small point.

[@CRL_One]

I think its pretty clear he was talking about bitmap pixels, not physical pixels of a display.

[@JiihaaS]

​@@CRL_One Exactly. Afaik the pixel data just contains the color and brightness information. Nothing about shape or size.

[@wischmopps293]

Stumpy Nubs - the channel of a woodworker analyzing topics in the same way as you. Same tone, same style, awesome. Are you brothers? You should make some kind of crossover ❤

[@jasonvytlacil1256]

masterclass

[@REKlaus]

Nice demonstration. What would be an interesting next step would be to do the same test with multiple frequencies being input simultaneously.

[@AudioUniversity]

That’s what he did with a square wave. A square wave is comprised of many frequencies.

[@AudioUniversity]

That’s what he did with a square wave. A square wave is comprised of many frequencies.

[@oyvindknustad]

Mind blown

[@someonesomewhere4446]

Dynamic Range ? For what ? We're living in Loudness War 😂😂😂

[@RealHomeRecording]

😅

[@MartinRonky]

Cheers

[@VyacheslavLogutin]

Stereo base of this video is enormous...

[@georgeellsworth3652]

This video could be useful in the discussion about the use of digital intermediaries in vinyl LP mastering, like the (overblown IMO) situation with MoFi. Hopefully, this is the end of that argument. But alas I know it won’t be…

[@benchociej2435]

It can be useful to use higher sample rates and bit depths in some production scenarios, but I'd say those aren't the typical cases. Still, even if it becomes necessary in production, the end user doesn't benefit from anything much better than about 44 kHz and maybe 19-20 bits in the absolute worst possible case (even then, the need for such a bit depth is questionable at best)

[@Artcore103]

As far as bit depth, I will add this, and maybe my description is inaccurate. 16bit is, as was clearly shown, absolutely more than adequate as far as the source material. I have many albums in both 16/44.1 and 24/96 for example, and have often compared them, as I'm sure many "audiophiles" have... but what people fail to consider is that typically, it's not the exact same master (that might exist at say 24/192, or 32/192 or whatever) that is simply converted or truncated to 16/44.1. When and if differences are audible, something else is the cause... a different mix, or a different master, or different post processing. BUT!!! When it comes to your playback system, namely your DAC and the settings of your playback program/device and that DAC, it can be absolutely beneficial to operate at 24bits, for one simple reason. In many cases, such as my own use case, people do not use analog volume attenuation alone, or at all. I do not use any analog volume attenuation - i have pure power amps with no volume controls, fed directly from a DAC (no preamp volume control either therefore). If the volume was not attenuated, it would be extremely loud, so my volume control is DIGITAL. Given the power of my amps and the sensitivity of my speakers, I'm using SIGNIFICANT amounts of digital attenuation. This, combined with the fact that while a DAC might be operating at 16 or 24 bits in theory, that assumes the system is operating perfectly and linearly, which it does not. ASR that publishes objective DAC measurements always shows their true snr/SINAD/effective bit depth capability, and the actual effective bit depth of the analog OUTPUT is always some fraction of the theoretical bit depth is that it's operating in digitally. So, combine those two facts, and you can easily experience for yourself, that a DAC operating in 16 bits with the use of digital attenuation into an unattenuated power amp WILL result in noise, especially with high sensitivity speakers (mine are over 90db). So, the source material can remain 16 bits, but we operate our DAC at 24 bits, because this upsampling allows for a lower noise floor that WILL be evident in this scenario. I don't think 32 bits is necessary even for this purpose... maybe with extremely high power amps and extremely sensitive speakers and therefore extreme digital attenuation, but I don't think that's practical or ever the case in a typical environment or use case. But 24bits, with an effective 18-20 bits (realistic for high quality DACs), is very useful in the above scenario. If you are using purely analog volume attenuation then it's probably not useful, but you also shouldn't be doing that. There is no analog volume control as transparent or "hi-fi" as using digital attenuation in a 24bits. Digital attenuation offers superior fidelity, and may also be helping your DAC's op-amps to be operating at a lower distortion as well, though you wouldn't want to go TOO low either, that's where an appropriate power amp watt rating is important, due to the non-linear performance of all amplifiers in that first 1% or so of their operating range especially. L/R channel balance also tends to suffer at high levels of analog attenuation, but not with digital. Setting the system to 24 bits doesn't make it sound better, it just adds zeros, but I can switch back and forth at will and at 16 bits the noise floor is higher. Exactly why this happens I'm not sure.

[@mdl555]

Great video, thank you ¡ I've got a question thou.... I thought that bit resolution has to do with the accuracy of the quantification of the samples.... I always compared it with a ruler: if my ruler only have centimeters, well, my measurements would be an approximation with lots of errors.... but if my ruler is divided in 1/10 of millimeters, my measurement, or the description of any sample in space, would be more accurate.... Am I wrong? Thanks and regards ¡

[@TheCito]

You’re absolutely not wrong. But, in your terms, if you approximate the measurement with your overly imprecise ruler, you would write down the approximation, in smaller steps than are on the ruler. But the DAC can’t, it just writes down the nearest “big step” that is on the ruler. Since the big steps are near enough in 16 bit, you will still hear a really close version of the sound, but the difference to the actual sound is heard as noise. This is, because a deviation up or down from the actual sine wave, is the same as if there would be another sound overlapping, that makes the deviations. And you don’t hear the deviations, you hear the sound version of them, the hissing noise. Thats of course completely oversimplified and someone please correct my possible errors that stem from the fact that I too just recently learned this and am no expert, or that English isn’t my first language… I hope this answers your question :)

[@JohnR31415]

Yes - and the errors are what we call quantisation noise. We can choose what this noise sounds like, tape hiss or shaped away from the most sensitive frequencies. If we do nothing it looks like a bunch of harmonic spikes…

[@MaskedDeath_]

In this case, your rulers are divided into micro- or even nanometers. Your measurement won't be any more precise after some cut-off point, because other than the ruler, you're also using your eyes.

[@user-nv4mj5rb4n]

The elephant in the room: who can prove that human hearing works exactly the same as the oscilloscope? The answer is: no-one.

[@Roger_Gadd]

For me there is an elephant dancing around the room on this topic. I am sure that plenty of people reading this know the answer and there must be plenty of resources online. But the issue I have is how is a clean band limit (low pass filter) performed that provides a presumably 96dB cut off over a mere 20% frequency increment from 20kHz without producing phase shifts that totally mangle any high frequency audio "square" wave.

[@MatthijsvanDuin]

Modern audio ADCs and DACs run at a much higher sample rate than the PCM sample rate and use a digital linear-phase FIR low-pass filter to achieve such a sharp cutoff with no phase distortion whatsoever. For example even cheap ($0.58) PCM1808 ADC has only ±0.05 dB passband ripple and a modest 65 dB stopband attenuation, while the PCM4202 has a ridiculous ±0.005 dB passband ripple and 100 dB stopband attenuation.

[@OrzoMondo]

I have a question: I always thought that a higher sample rate allows a more gentle sloping filter, because the side bands are farther away. Is this a valid argument? For example, in the video you have a filter at 20.5 Khz whose roll-off is -100 dB at 21 KHz (if I interpret this correctly). That's an insanely sharp filter, which you need because theoretically your next band starts at 22 KHz. If you sampled at 96 KHz, your next band would start at 48 KHz, so your filter could roll-off much more gently from 22k to 48k, which implies that in the bandpass portion, the filter would be much flatter.

[@moe.m]

That is true, and one of the reasons why recording mixing and mastering is often done with higher sampling rates. However, after mixing and mastering, this is not needed anymore and you can store the sound in CD quality. For playback, there are oversampling DACs which move part of the filter to the digital domain, then you can have a much simpler analog filter afterwards.

[@JohnR31415]

Most inputs over sample *massively* since a (cheap) analogue filter can bandlimit over 100kHz, sample at 300kHz then an extremely cheap digitally band limit down to something more reasonable (like 48kHz) for the rest of the processing. Trying to get an analogue filter to leave 20kHz alone and let nothing over 22kHz though would be very expensive.

[@neodonkey]

@@JohnR31415 Even in the 90s I remember CD players would boast like 8x oversampling, presumably as you say so they could implement reasonable cost filters.

[@Kavukamari]

honestly, I think see through cases on electronics IS ideal transparency

[@someonesomewhere4446]

Extremly fat episode ❤❤❤

[@andythebritton]

This is very good, but I'd like to know more about how the DAC achieves the smooth output given it has only the discreet 'lollipop' values to work with. Monty makes the point that there is only one 'solution' given the sample values, but how does the DAC find that solution?

[@PippPriss]

This happens via interpolation, if you Are into electronics you may find a schematic or a helpful video on this topic. Basically, if we are absolutely breaking this down to ground zero, there has to be either a capacitive or inductive element, since these are the only time based basic components you can place into a schematic

[@andythebritton]

@@PippPriss thanks. I vaguely understand how a capacitor can be used to smooth out a signal (e.g. in an AC to DC power supply following the rectifier stage) Is that the sort of thing?

[@DolphinWave]

The DAC doesn't "find" the solution. It's simply the only solution that exists, giving spectral constraints of a signal. Any other signal shape going through those quantization points will have a different spectral output, that can't exist because it goes beyond the Nyquist cutoff range. Basically, the low pass filter beyond Nyquist frequency is what cutting out all other solutions, leaving the only one that can exist.

[@MatthijsvanDuin]

@@PippPriss nowadays the interpolation is mostly done digitally in the DAC. it would be very difficult and expensive to make an analog low-pass filter which does a decent job at passing everything below 20 kHz basically unmodified (including phase) while strongly attenuating anything above 24.1 kHz

[@yjweaver5108]

What software was the thinkpad using ?

[@dirg3music]

Fedora Linux seems to be the OS given the F in the top left corner.

[@abergmann]

23:40

[@cnr_0778]

An ancient version of Fedora Linux running the Gnome 3 UI.

[@nahblue]

I'm guessing Monty built that interface and the demos himself

[@doryiii]

gnome 3 (gnome shell) when it first came out.

[@NicleT]

This is very enlightening! But by the time a sound is recorded in the computer at less than 44kHz, more I edit and save it, more it degrades. So the problem is really _in the box._ but I would be curious to see your setup analyzing a recorded sound instead of the line chain

[@benchociej2435]

Well yeah, if you sample audio below the 2*Nyquist it's going to lose information

[@MatthijsvanDuin]

"more I edit and save it, more it degrades" ... that sounds more like a problem of insufficient bit depth or poorly implemented audio processing algorithms, but it depends on what exactly you mean by "edit". it's definitely a good idea to use more than 16-bit depth during editing to avoid repeated quantization noise (32-bit float would be a typical choice), even if 16-bit is fine for the final end product. using 44.1 _shouldn't_ be a problem or result in degradation if the audio processing is implemented competently, but using 88.2 or 96 kHz sample rate allows certain types of filtering (e.g. fractional delays) to be implemented with much better performance for the same quality (despite having to process twice as many samples), which may mean better quality if the programmer prioritized performance over quality.

[@Tyco072]

Very interesting. But how does a 20KHz square or saw tooth wave look at 44,1KHz sampling? Since there is only 1 sample for each half wave, the output at 20 KHz can be only a sine wave, independently by the input wave form. This would mean an unacceptable distortion. Or am I wrong? Also between 10-15 KHz, where there are only 1,5-2 samples per half wave, the distortion would be very high if the wave form is not a pure sine. Could you show how it would look like? It would be very interesting.

[@Tyco072]

@@nicksterj Hi. It is very interesting. This aspect is never well explained in. The common assertion "44 KHz sampling can reproduce precisely all signals up to 20 KHz" is deeply wrong. It is true only for a pure sine signal. Since above 10 KHz there is headroom only for the 2nd harmonic (20 KHz), it should mean that all the non sine wave forms get rapidly distorted above 10 KHz, heavily, on CD and analog formats. The analog formats for consumer use have less useful bandwidth than CD, then it should be even worst. It would be interesting to show how pure non-sine wave forms get distorted rising up with the frequency up to 20 KHz and how much the difference is audible.

[@Tyco072]

​@@nicksterj "you must sample at more than 2x the highest frequency contained in the signal in order to reproduce it fully". This is exactly the point that never is quoted and clear explained in the videos about digital recording and analog bandwidth (for the analog formats). Only sine waves are shown. It would be interesting to see how the non-sine signals get distorted above 10 kHz, with different sampling rate and bandwidth (for analog formats) and how much the difference is audible (if it is audible). It would be funny to hear a heavily rounded 11 kHz square or saw tooth wave, but don't hear the difference to the full shaped wave. Yes, you don't hear the harmonic above 20 kHz, but in theory you could/should hear the difference in the shape of the waveform at 10 kHz, if the difference is much (perhaps this is the crucial question). I am only curious to test these effects. I am not supporting the myth that vinyl sounds better than CD because of the 20 kHz cutoff, since the frequencies above 18 kHz are already so attenuated on vinyl, they they don't play a role, and I never heard more fine details (always less) in a vinyl than on a CD.

[@Tyco072]

@@nicksterj I watched it, but the square wave in the video is only 1kHz, it looks still pretty square. It is not the comparison I mean.

[@Tyco072]

@@nicksterj Thank you! I missed that video on that channel. It is what I wanted see.

[@duprie37]

Band limiting: why am I reminded of Feynman diagrams and renormalization...

[@RAFMnBgaming]

What do fractional bit depths mean?

[@MatthijsvanDuin]

n-bit depth means the full range is divided into 2^n quantization levels, or said differently the bit depth is log₂(number of quantization levels). but there's no reason the number of quantization levels _has_ to be a power of two, and if it isn't then you end up with a non-integer bit depth.

[@RAFMnBgaming]

@@MatthijsvanDuin ok but in terms of storage, in an uncompressed audio file, what would fractional bit depth audio be represented as? Or is it equivalent to compressing it?

[@MatthijsvanDuin]

@@RAFMnBgaming While normally the main reason to reduce bit depth would be to reduce file size or bitrate, he's doing it just to demonstrate the effects of quantization so most likely he's still using 24-bit or 32-bit for the samples but with a subset of the levels used. To give an example using small numbers: if you're using 8-bit word size (range -128…127) but only use the levels -128, -77, -26, 25, 76, and 127 then you have log₂(6) ≈ 2.6 bits of effective resolution. Having said that, if you really want to it's most certainly possible to efficiently store a signal at that resolution. While a single sample would still require 3 bits to store, you can pack 5 samples into 13 bits (or 40 samples into 13 bytes) to achieve 2.6 bits/sample of actual filesize.

[@Norstator]

This is the kind of content audiophiles avoid.

[@izerpizer]

You really should unlist this video; It is phenomenal.

[@cyberkexx]

Interestingly enough, you preferred to hide bandwidth-limited Heaviside step function under the carpet :-) In physical world, it is easily emulated by the flick of the switch, but once you limit it's bandwidth, it's representation will be non-zero even before you flick it, as if your filter-sampler "knew" beforehead that you are going to flick it.

[@larbidinari5937]

This video looks like it was made in the 90s, great video though

[@leyasep5919]

the Thinkpad says 2012 😀

[@synthshoot1026]

The original link in the description looks better. KZbin resize may blur things.

[@FirstLast-is9xe]

Try the same with very low frequencies! 20 to 80 Hertz

[@clehaxze]

The math also woks. It's still below NyQuil frequency. However the equipments might have issue displaying them. Remember these are designed for electronics. They usually operate at MHz or GHz levels. Also the spectrum analyzer needs a very large window to display spectrums around 20Hz.

[@MelanieMaguire]

I would prefer to see this demonstration using a real piece of music (lots of instruments all playing together) instead of a single sine wave. Convert analog to digital, then back again and compare by overlaying the waveform. If anyone reads this and does this experiment, please comment here to let me know, so I can watch it. Thanks!

[@tronam]

It wouldn’t make a difference how many signals are merged together because the final output is still just a single waveform… and it still wouldn’t be a digital stair-step, because it never was to begin with.

[@user-lh1fw6qh4d]

44.1/16 is enough for good audio quality? Well, yes, it was established some 40 years ago. But the whole presentation is not OK, manipulating facts to prove your point is not scientific by any means. 1) Even 10% THD is not so obvious on the oscilloscope, so comparing waveforms on the oscilloscope and saying they are identical is pointless. 2) The ADC in the audio interface used almost certainly has sigma-delta architecture and it's real sampling frequency (and Nyquist frequency) is 64 or more times higher than output data rate aka sampling frequency in recorded file. And the whole sampled signal is filtered digitally before recording to file. 3) There is nothing that is infinitely small that can be implemented in real electronic system. The signal at the output of DAC is a stairstep signal anyway. Then it is passed through a LPF to restore a smooth waveform, that is shown on the oscilloscope. What is not shown nor said is that oversampling and interpolation in digital domain is performed prior to DAC so that the waveform may be restored accurately using feasible filter designs. So the signal at the output of DAC is not 44.1/16, in most cases it is 352.8/20 or higher. And so on and so forth.

[@christopherdunn317]

I bet you back then when they started this digital thing ? they did the same thing with the same equipment , and that's why they settled for 16bit 44.1khz MR HONG KONG down below anti aliasing ? Ya thats for video graphics to smooth out jagged edges not fix a so called stair step LOL !

[@KokHongSoh]

The stair step is removed by the anti-alias filter (low pass filter). All CD players have such a filter at the DAC output. That is why the stair step is not observed at the output.

[@benchociej2435]

There would be no stairstep even without a low pass filter. Depending on implementation there would simply be more harmonic distortion.

[@MultiBallchinian]

​@@benchociej2435how can that be true? We saw the samples of the analog wave. When each of the samples is written to the DAC, it will adjust it's output to that voltage until the next sample is written. Without a low pass filter, we would see the stair steps between each sample.

[@benchociej2435]

@@MultiBallchinian DAC hardware can't make a stairstep. Nothing truly can, but typical DACs don't even come close as they might have a designed high end frequency response in the 40 kHz range (even before filtering). That's because real world components always have some reactance (capacitance or inductance). This means that amplifiers have a limit to the product of gain times bandwidth. Even if the DAC had massively overspec'd components, you could only ever get harmonics that somewhat approximate a stairstep.

[@MultiBallchinian]

@@benchociej2435 this still doesn't explain why the sin wave is recreated perfectly at various frequencies. I understand that the DAC output can't have an instant rise time between two codes, but i am confused as to why the DAC's rise time between two codes perfectly matches the sine wave.

[@SoundAround-gr2xi]

I finally did the measurement and it seems that modern soundcards are sine wave generators and I also found side effect of this AI " kzbin.info/www/bejne/hWrLi2p9mK5nqMk ".

[@MatthijsvanDuin]

it has nothing to do with AI, it's just math. the fact that the original waveform can be recovered is (as Monty explains) the result of it being bandlimited, this is the result of the "Nyquist-Shannon sampling theorem". it's also not hard to implement (if you don't care about optimization), like 10-20 lines of code and a lookup table (containing the impulse response of an appropriate low-pass FIR filter).

[@ChaseAlberti]

There should be a stairstep pattern there? The values here are really really small, the full range of a 16-bit DAC would be 2^16 or 65536 values. Assuming a VREF of 2048 mV (using a common value in embedded systems) the 16-bits would translate to 0.03125 mV. With an 8-bit DAC the minimum step would then be 8 mV; much larger but still much smaller than what can be easily seen on the oscilloscope. The value of the DAC cannot change instantaneously; however, there may be enough capacitance on the output to smooth the waveform enough. Another important note is what is the frequency of the DAC? The sampling rate of the ADC doesn't necessarily correlate, so the DAC could be clocked much faster. Would also be curious on a direct comparison of a FFT on the input and output. Not trying to argue but genuinely curious, definitely agree that 16-bits and a ~40 kHz sampling rate are good enough for the vast majority of listeners. Great demo, on the square wave that would be great for an EE Comms class!

[@moe.m]

There is no stair step pattern. As was said in the video, a signal with a stair step pattern might be part of the conversion, but that is not the finished signal. You will have a low pass filter afterwards and the signal will be smooth.

[@ChaseAlberti]

@@moe.m A low-pass filter doesn't magically make a "stair step" the output of the DAC into a perfect sine wave like that. I'm saying if you zoom in far enough you will see some "stair-steps" albeit they will very very small. That's why I also mentioned comparing the input and output FFT's, you will see that noise is added into the system (everything adds noise even filters) and see some more harmonics generated from the quantization.

[@woodcoast5026]

@@ChaseAlberti The frequency components of the stair steps start at 40Hz and the Low pass filter starts at 20Khz and so it does not filter them out. For a basic D to A without oversampling the steps are there after the reconstruction filter. They are innocuous if dither has been used. In a modern D to A they are not there because modern converters add extra steps that change quickly, quickly enough to be filtered out by the reconstruction filter.

[@serenity1378]

@@ChaseAlberti The entire point of the video is that there is not a stair step. That's a misrepresentation of the signal the same way pixels are not squares. They are discrete points of information. Only one signal can pass through all of those points of information and still be valid, thus recreating the signal from those points of information perfectly is not only possible, but the only option.

[@ChaseAlberti]

​@@woodcoast5026 Oh okay, so essentially the DAC is way oversampled and the low pass filter dampens the "spurs" / steps. Although, a filter can only dampen the steps, so if you "zoom-in" far enough you will be able to see the transition between values. Also, curious to know which DAC is used and I would think it would be a Sigma-Delta because of the lack-of-cost.

[@daniwalmsley611]

I loved this, very interesting very informative I disagree that this offers any sort of conclusive proof. You mentioned "just because we can measure something doesn't mean we can hear it" but the reverse is also true. Just because we cannot measure something doesn't mean we can't hear it. It's easy to have hubris and say our testing equipment can measure beyond what humans can hear. But it is important to remember that it is possible there is an unknown variable. Jitter was once an unknown variable and products dealing with it labled as snake oil, but we have since been abke to measure it and deal with it. Anyway, my issue lies with application of the niquist sharron sampling theorem. It requires that all the composite sine waves be below 20khz (the upper limit of human hearing) for a 44.1khz sample rate. On the surface this is reasonable, but you have lresented no evidence to suggest that this is how humans hear. If ultra sonic frequencies were present it is theoretically possible that they distort the audible frequencies in an audible way. But this is conjecture. It's entirely possible that any ultrasonic interference be in audible, it's a matter for psychoacoustics not engineers I loved the video though, it did a great job of showcasing the niquist theorem and the most contentious topic of the lack of square/ladder waves

[@daniwalmsley611]

@@nicksterj if we can hear it then we can measure it, that doesn't mean we know how to measure it, or that the people attempting to measure it have adequate testing methodology. There is no substitute for blind listening tests

[@kennyxkazuki713]

I am the 666th like lol

[@SoundAround-gr2xi]

Impossible. No way that you first sample is +0.5V then second is -1V on input and on output you will get +1.41V , makes no sense, there must be some trick. Either it has harmonic frequency MIDI optimalisator ON or there is oversampling with 192KHZ and showing only 44.1kHz step form or other trick.

[@menocorde]

It's called maths. Welcome to science.

[@relatively_random4903]

He's wrong about digital images. Love the video though. Pixels actually do represent the average intensity across the square surface, not a single value at a point. You could in principle measure air pressure at an infinitesimal point in time for sound, but light is different. It's a bunch of particles randomly hitting a surface. If you give them an infinitesimally small target, the probability of hitting it will always be zero.

[@menocorde]

Yes, but he means this in a mathematical sense. Think of an array, It's about the way you display the meaning of those pixels that give meaning to an image. We choose to display squares of different color and light intesity adjacent to one another because that makes the most sense, but we could as well, as he explains on the video, no display it that way, such as the way that nowdays screens made up of tiny leds separated mm apart can create an image if you stand far away enough

[@relatively_random4903]

@@menocorde My point is that flat squares are the more correct way to display pixels, unlike in audio where infinitesimal points are a more accurate description of what values were actually measured. It's not just arbitrary, it has implications for how the data behaves. For instance, because audio is a collection of infinitesimal samples, you can get aliasing unless you filter the analog signal first. Digital images don't get aliasing because each pixel takes the average intensity in its area and so have filtering inbuilt. (Bayer grid sensors do get aliasing because they skip pixels for each color, but that's a complication that doesn't apply to classic grayscale and triple sensor cameras.)

So there are no stair-steps but it still gets jagged when quantized. This means higher resolution still has a point. I think the debunking video which led me here is misleading. ( kzbin.info/www/bejne/mXWainmLjrGjesU )

[@NamelessSmile]

When?

@@NamelessSmile When he says 16 bit/44.1 kHz is just as good -if not better-. I understand that most people won't hear a difference but it's certainly not better nor the same. Stating these are unnecessary and might be misleading for some. Telling that we can't hear a difference for most applications is enough.

[@pvandck]

@ kzbin.info/www/bejne/mXWainmLjrGjesU

@@NamelessSmile If you ask for what application a higher resolution would might be needed, I can give an example that gaming or simulation purposes. For example a gunshot is more than 150 dB. If you want to reproduce such high SPL, you need to crank up the volume, And if you do that you will definitely hear the noise floor with a 120 dB dynamic range.

[@NamelessSmile]

@ surely in that rather strange example, the noise of the (even high quality) analog amplification stages would vastly outweigh the quantisation noise from a 16 bit system ?

[@Fitzrovialitter]

This excellent presentation by Monty is years old; why are you claiming it's new on your own channel?

[@WarrenGuy]

He didn't.

[@serenity1378]

Please read up on what Creative Commons is. And also read the description which does not have the phrase "new" anywhere on it. And also just, learn about the FOSS and Libre communities in general.

[@Fitzrovialitter]

@@serenity1378 KZbin presented me on this channel with Monty's ancient - yet welcome - video as a new upload.

[@Fitzrovialitter]

@@serenity1378 As a software developer for fifty years I am familiar with its idioms.

[@serenity1378]

​@@Fitzrovialitter Then why say what you did?