Nyquist-Shannon; The Backbone of Digital Sound

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Let’s talk a bit more about digital sound. Thanks to a mathematical theorem, we know that a bandlimited signal can perfectly be represented by a series of discrete samples that occur at twice the rate of the frequency of the bandlimit. OK, that’s hard to explain in a little descroption blurb, so the video is probably your best bet.
This here is the video of Monty’s. YOU SHOULD TOTALLY WATCH IT!! There is so much good stuff in here and it’s a great resource for dispelling some of the myths of Digital Sound.
• D/A and A/D | Digital ...
This is his original article that inspired the video (I think--it’s a great article anyway):
xiph.org/~xiphmont/demo/neil-...
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2 июн 2024

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Комментарии : 2,3 тыс.

@OptimumPx 5 лет назад

"Don't worry about it." -Technology Connections 2018

@littlegandhi1199 5 лет назад

You can't worry about it. You don't have a choice between some oscillations and none unless you're going to invent a new technology. He pointed out how both analog and digital are exactly equally faulty in this sense.

@OptimumPx 5 лет назад

You're taking my comment _waaay_ too seriously. I merely found the phase's use in thia video funny.

@ToMeK3001pro 5 лет назад

what timing?

@isidoreaerys8745 4 года назад

“So the key here is: Don’t worry about it!”

@pilotavery 4 года назад

@@littlegandhi1199 It's not faulty. That's just how analog sounds happen in the real world. It's that if you could project a perfect square wave, your ears will still have those ocilations. Because your eardrum can not physically teleport from the top to the bottom of the canal.

@TechnologyConnections 5 лет назад

There's a shot in this video that's upside down because... I forgot to un-upside down it. Sigh.

@K-o-R 5 лет назад

That is, in fact, the technical term for it. It's under Clip > Transform > Un-upside-down.

@Pistoletjes 5 лет назад

5:01, I presume?

@mukiex4413 5 лет назад

Oh wow, I didn't even notice. I just thought it was part of the presentation =D

@El_Grincho 5 лет назад

You have to cater the antipodes as well.

@schadenfreudebuddha 5 лет назад

In VideoPad, it's called re-rightsideupify

@Jetsetlemming 5 лет назад

The hardest part of how sound works for me was how multiple sound sources combine to a single data stream, a single wave form. Everything an ear hears is the input of a single wave traveling through the liquid of your cochlea, and your brain does extremely complicated processing on it to separate those elements, identify them, and locate them in 3d space. This is why your headphones don't need separate audio outputs for every instrument in the song you're listening to.

@C.I... 5 лет назад

Yes that's right. There are 3 ways the brain separates the position of sounds with the help of our 2 ears. 1. Difference in volume 2. Difference in time 3. Difference in timbre The first point is pretty self explanatory. The second point relies on the distance between our ears and the fact that there will be a time difference left to right (or vice versa) between any sounds that are to the left/right of you. If two similar sounds arrive at your ears within 50ms of each other, then your brain uses this difference and interprets it as a position, favouring the side that received the sound first. Any longer and you will hear two separate sounds. The third relies on the fact that if a sound directly hits one ear, then your head will "shield" the other ear from the higher frequencies in the sound. This is because higher frequencies are more directional than low frequencies and are less likely to "bend" around your head. The side with more high frequency content is interpreted by your brain as being more likely to have heard the sound first.

@Jetsetlemming 5 лет назад

C. H. The biology and high level concepts are fascinating and I can comprehend them pretty well. The physics, though, that's another story. The way multiple sound waves combine into a single two dimensional signal that still works for us as they're still distinct is the hard part. Harmonics, different sounds interacting by being amplified or cancelled out, etc. All that physical stuff that happens in between the 100 piece orchestra and the microphone turning their combined work into single series of numbers (or two for stereo :p)

@C.I... 5 лет назад

I believe it's as simple as summing them. In the digital recording domain you've got a hard top limit to go by as well, so if you're using a basic DAW you're averaging the values and then amplifying them (or not) depending on how mush headroom you have. Newer DAWs with 64-bit internal precision mean that the summing can just happen without the master fader ever clipping.

@806cat 5 лет назад

This is also why you can have lossy coding like MP3 and it still sounds fine.

@Falcrist 5 лет назад

Just like a fourier series, it is indeed just as simple as summing them.

@MostlyPennyCat 5 лет назад

This is how I like to think of low pass filters "de-jaggying" (antialiasing). A low pass filter, at it's absolute simplest, is a capacitor (with a current limiting resistor to keep the smoke in) Capacitors resist change in voltage. Like a weight on a spring resists change in length of a vertical spring. So that infinite rate change stair step is slowed down by the capacitor. That's it. The digital signal tells the voltage to "CHANGE RIGHT NOW NOW NOW GO GO GO" Then the capacitor replies, "OK, will do, gimme a second, I'm getting there, plod plod plod" Simples.

@gianluca.g 5 лет назад

assuming that voltage is torque and current is rotation speed, I like to think to the capacitor as the spring and the inductor as the flywheel. In fact, the equations governing them are pretty much the same

@DRSDavidSoft 5 лет назад

Gianluca Ghettini this is like a perfect analogy!

@TiagoTiagoT 5 лет назад

Wouldn't that be inductors? Or am I reading it wrong?

@gianluca.g 5 лет назад

TiagoTiago yes, my bad. Updated!

@MostlyPennyCat 5 лет назад

Gianluca Ghettini Ok, I get a flywheel resisting change in RPM. I get torque being Voltage. What is this spring? And how is it resisting change in torque? Is it between the torque source and the drive shaft? Is it line with the drive shaft and stores torque as potential? Also, is this instead of my analogy of a weight on a spring? It probably would have better maths because I guess it's polar maths? Amd when you watch the voltage try to track the digital input you're watching the flywheel edge on, rotated 90 through the vertical?

@thecommenter4629 4 года назад

I was a young lad when CD's became big but I can still remember the first time I heard a CD back in the late 80's... sounded like the musicians were in the room with me. To my ears it was superior to any cassette tape or vinyl record because there was no background noise... just a clarity of sound I had not experienced until then.

@K-o-R 5 лет назад

"wiggly wobblies" I told you to cut out the technobabble!

@Jackpkmn 5 лет назад

+mohomed1208 i hear it's reached a very high level of development, its THE FUTURE

@RCAvhstape 5 лет назад

It's as bad as Dr. Who's timey wimey stuff.

@SnabbKassa 3 года назад

All hands on deck! Swirly-thing alert!

@OkuriLucy 3 года назад

is it timey wimey?

@AnnaVannieuwenhuyse 5 лет назад

The Nyquist-Shannon theory is one of my favourite. It just can't be questioned. It just is solid mathematics.

@Myrtone 5 лет назад

While it can't be questioned, about about the effects of dithering.

@pilotavery 4 года назад

Some people can hear above 20khz though... Solution? 48khz instead of 44.1

@aldeywahyuputra5719 4 года назад

Dalton what’s funny is that it’s possible that what the ‘audiophools’ are referring to a ‘more perfect’ of vinyl sounds is actually the imperfections that limits the analog signal: physical defects.

@a64738 4 года назад

@@pilotavery Just going up to 48khz helps a lot, CDs 44khz make everything over 15khz sould more and more like noise where 20khz sound 100% like noise if it is more complicated then a pure sine wave...

@DaveGOfield 4 года назад

@@a64738 Oversampling does in fact change the signal to noise ratio, I like a crisp high end but I question the "musical" application of frequencies over 20KHz...

@CapyTapy 5 лет назад

Xiph Monty? The same Monty from the opus and vorbis codecs? Damn this dude deserves an award!

@d1oftwins 5 лет назад

Yes, that Monty. :)

@japzone 5 лет назад

Plus a hug for those royalty free codecs.

@DavidLeeKersey 5 лет назад

Monty also has a good video that explains A/D and D/A conversion. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-cIQ9IXSUzuM.html

@lemondropcentral14 Год назад

I have a 4 year physics degree and have worked as an electronic testing engineer for the avionics industry for 2 years.... this video finally helped me understand what the Fourier transform does. Sure, I used it all the time on my physics and math homework in college, but I could never wrap my head around what it actually does. After this video, it finally makes sense!

@megamaser 7 месяцев назад

This is hard to believe. You worked them out by hand all the time without knowing the basic idea of what it is? In my physics bachelors, I didn't use them "all the time." I used Fourier series in probably one or two classes.

@shmehfleh3115 5 лет назад

The Covox Speech Thing and Disney Sound Source are two practical examples of really simple ladder resistor DACs. They both plugged into the parallel port of an old PC and used its 8 data lines to drive 8 resistor networks tied into a mono analog audio out. This chumpy setup basically created an 8-bit DAC with a sample rate that was limited only by the speed of the parallel port. Unfortunately, as they were completely dumb hunks of passive electronics, they couldn't tell the difference between data meant to be converted into sound and data meant for the printer. If their output was left on when printing, they made a horrible squealing noise.

@metalzizar 8 месяцев назад

That Monthy video on digital audio is the holy grail for us who want to learn deeply about the topic, without getting too complicated with the mathematical part of it.

@scruffythejanitor1969 5 лет назад

I request one in-depth video on DACs, please. Or whatever, since you've yet to have a bad video on this channel.

@Asdayasman 5 лет назад

Agreed, everything he does is gold. I'd like to see a Technology Connections video on peanut butter just to see what he does with it.

@ai4px 5 лет назад

I suggested the CD.... EFM, hilman diffie encoding, tracking, focus etc.... fits right in with your DAC suggestion.

@MJ-uk6lu 5 лет назад

That's pretty much this video. If your DAC is poor then reproduction won't be in such a nice waves as were shown here and there will be more artifacts (inaccuracies).

@Asdayasman 5 лет назад

@fred I sure do, it's just a little more developed than a 10 year old's.

@Jeff-Russ 5 лет назад

You see one in action if you use the falstad circuit simulator, click on the "Circuit" menu -> "Analog/Digital" and load up a DAC like the R-2R Ladder DAC. www.falstad.com/circuit/circuitjs.html

@richarddeese1991 4 года назад

Thanks! Claude Shannon is absolutely an unsung hero. He should be as famous as Von Neumann (to me)! He was clearly a genius, and - more than any other person - is the father of information theory. He laid the groundwork for the digital age, and he did it back in the 1940s. tavi.

@ReikazeRambles 5 лет назад

I've been a fan of technology connections for the longest time and have been watching the channel for fun, but I never expected it to explain a topic in one of my classes better than my professor! What a pleasant suprise, thanks for the video :)

@GenXGrownUp 5 лет назад

"The key here is... don't worry about it." Had me literally laughing out loud. Thanks again for these awesome videos. You inspire me to work harder on my own channel's production and entertainment value. 😀

@jfbaquero 5 лет назад

And yet another great video. I had read Monty's article eons ago, for a long time I had lost track of it. As an audiophile I used to share it with other audiophiles to help them understand how digital audio works and also help explain why buying audio downloads sampled at 192kHz is just a waste of money (maybe not for Batman). The reality is that almost no one understands the math and engineering underneath (including some engineers). The problem usually is a lousy ADC/DAC not the digital medium. Your lecture in this video is the closest I 've seen to make such complex issue understandable for those who lack the science background. Amazing work! Respect and Thanks!

@RenePatrique 5 лет назад

Really had to LOL about the "Batman" reference in your comment! - :D - Made my day! - Cheers!

@videodistro 4 года назад

His video clearly shows the issues is completely misunderstood. Now, beyond the arithmetics of audio, let's get.deeper into audio itself. I was educated in sample rate affects by THE Rupert Neve. If you don't know his name, you don't know audio. Look him up. Anyhow, he can show the affect of higher sample rates (frequency) based on overtones and how they can affect what we can hear directly through physics. I have heard EXACTLY what he is taking about through experience, and no, I don't claim to be a geeky audiophile. You just have to listen. Overtones above our hearing threshold affect frequencies within our hearing threshold. Those who smugly tell you "you can't possibly hear above 20 kHz" are only partly right, but significantly wrong when it comes to what those frequencies can do to other frequencies. Simpletons don't know this and say its "just audiophiles acting snobbish" when in reality they just don't have the wider experience and education on audio (analog) and physics. It's more complex than the Nyquist theory and the digital side of things. Sad that this is not more widely understood.

@kaitlyn__L 4 года назад

@@videodistro I've read things saying those are just unwanted harmonics within the amplifier or speaker, and when the file is accurately output, they are no longer present. What's your take on that?

@hand__banana 2 года назад

there's a reason audiophiles dont blindly abx test these things and then use nebulous terms to describe differences between certain dacs.

@marksmith2913 2 года назад

@@hand__banana Bingo!

@LMacNeill 5 лет назад

*Very* cool explanation of the Nyquist-Shannon theorem. Made it easy to wrap my head around it. Thanks!

@Myrtone 5 лет назад

Yes, but the sufficient condition given isn't quite right. A sample rate exactly twice the highest frequency suppresses that frequency whole or in part, depending on the phase, and unless the samples fall right on peaks.

@benuscore8780 5 лет назад

This whole time I've been wondering what happens if the samplerate falls out of phase...

@Myrtone 5 лет назад

A series of samples going high-mid-low-mid-high describes a frequency of a quarter of the sampling rate. A series going high-high-low-low-high-high also describes the same number of samples per cycle but at a different phase. If the sampling rate is an integer multiple of the frequency described, the exact pattern of samples depends on relative phase.

@this.is.lapc506 5 лет назад

The work of the low pass filter is producing analog integration of signals... seems to me.

@larrytroxler7017 2 года назад

Yeah, too bad he got it wrong.

@jacekjagosz 5 лет назад

Wow, this is an eye opening video! Like how DAC is a resistor ladder, it is so simple!

@SeverityOne 5 лет назад

I've seen a DAC that plugged into the parallel port and simply had a bunch of identical resistors soldered to the output pins. Not the most professional solution, but this was the early 1990s, and people didn't have sound cards lying about.

@Trafo888 5 лет назад

You think about COVOX.

@El_Grincho 5 лет назад

That was most likely a R2R-ladder. See en.wikipedia.org/wiki/Resistor_ladder#R%E2%80%932R_resistor_ladder_network_(digital_to_analog_conversion)

@mikosoft 5 лет назад

Most common DACs today are not resistor ladder because they're actually quite complicated. Most are sigma-delta these days.

@El_Grincho 5 лет назад

Yup, the raspberry doesn't have an analogue out - it uses either PWM or Sigma-Delta. However, one-bit CD-players(MASH) are quite old, and SACD is 1 bit.

@NickMoore 5 лет назад

Band-limiting was the conceptual bit I have been missing for ages! Thank you for putting it all together.

@tombax1653 5 лет назад

Agreed. That was the keystone that tied it all together for me too. Man this guy is awesome!

@SuperFlashDriver 19 дней назад

The low pass filter in my opinion was the one that I had the hardest time understanding, and probably, for many of my digital audio recorders, never bothered to used because I wanted to edit it myself and have it be recorded totally RAW and with no effects included in the audio and such, except the intensities of the audio and such (This is why when I go to concerts, I put it at the low volume so it doesn't end up distorting, compared to classroom sessions where I put it on medium, but it picks up a ton of fan noise in the background, which sucks but that's what it is sadly).

@laurensweyn 3 года назад

Man, I remember learning about Nyquist's sampling theory in an engineering class and being pretty sceptical as to how that would actually work. We were told to just accept it at the time but this makes it so much more logical!

@MalachiTheBowlingGod 5 лет назад

You just angered every single audiophile on the entire planet! :o Also, I've heard the graph called a 'lollipop graph' - because it's representing sampled points, not an actual curve.

@inertia186 5 лет назад

I'm so glad you said "giant leap" instead of "quantum leap." It bugs me when people say "quantum leap" because it's the smallest possible change that can be detected in chemistry.

@llary 5 лет назад

inertia186 I think you'll find it's actually a time travel comedy drama with a catchy theme tune.

@inertia186 5 лет назад

Oh boy.

@thebeststooge 5 лет назад

Same nonsense as using Ultimate to mean the best when it, in fact, means final as in the Ultimate destination.

@K-o-R 5 лет назад

True, but if something is the best then clearly you won't need another version of whatever said thing is because it's already as good as it can be.

@williamapodaca8614 5 лет назад

I'm pretty sure it's in reference to how much QFT changed how we view the universe

@CatsMeowPaw 5 лет назад

650Mb was a lot of data. When I bought my first CDR writer in 1997, my entire hard drive was only 2Gb in size. CDs represented an absurdly cheap way to store data. Fast forward to today... and that's no longer the case even for dual layer blu-rays, which are far more expensive per gigabyte than hard drives.

@lawrencedoliveiro9104 5 лет назад

Particularly since PC hard drives of the period were only on the order of tens of megabytes. This was a particular issue to those trying to create CD-ROMs. Even when DVDs first came out, they held more than the common hard drive capacity, though the ratio was smaller. By about the ’00s, hard drives had overtaken optical media and left them in the dust.

@nthgth 4 года назад

@@lawrencedoliveiro9104 but there's still no cheaper way to give someone some music they might like to listen to in their car

@lawrencedoliveiro9104 4 года назад

The car I’ve been driving lately (newer than my own) has no CD player, but it does have Bluetooth and USB ports.

@loganricherson3749 2 года назад

@@nthgth I mean, you could download it on your phone which has a cheaper storage to cost ratio

@richardiredale3128 2 года назад

A purist will point out that it's 650 MB, not 650 Mb. Megabytes, not megabits. Huge difference. But I'm not that fussy.

@MichaelW.1980 Год назад

I am very glad that years ago a hobbyist musician took me under his wings and had bulletproof arguments against a sound card I wanted to buy back then and that was acclaimed by lots of audiophiles. He pretty much debunked their marketing slang and made me see it for what it was. An overly expensive consumer device. This made me explore the rabbit hole of digital audio. And now I’m here, glad to find a well produced video aiming to debunk another myth I used to believe in back then. Thank you!

@mpuppet1975 4 года назад

I always assumed the "stair stepping" would never reach the output, basically because DAC is not a misnomer. If it says it puts analog out, it puts analog out.

@BrianMarshall1 3 года назад

A discrete voltage is still analog.

@thomasb1337 2 года назад

@@BrianMarshall1 that's why I've had my professor at school explain to me and our class that for digital signals, digital is just a layer over analouge. We just interpret voltage levels as digital data. That's why noise/interference can be harmful to a digital signal. Even if the data is right, noise/interference can cuase the bits to flip.

@kamalmanzukie 2 года назад

nope, there is definitely spectra associated with outputting a jagged signal. ('infinite' mirrors of the baseband signal), and basically we remove all that with analog filters to get the 'perfect reconstruction'

@jgseg6828 3 года назад

Audiophiles are the flat earthers of music. I hope some watch this formidable explanation and accept the hard facts of physics and maths, leaving behind some mambo jambo mojo mythology about digital being worse than analog.

@zaphodsbluecar9518 2 года назад

"Audiophiles are the flat earthers of music". I love it! (I'm also stealing it...). :-)

@jgseg6828 2 года назад

@@zaphodsbluecar9518 You're very welcome! LOL

@alexschoenfelder-lopez4374 2 года назад

Not all audiophiles... Take a look at .FLAC vs mp3 so digital audiophiles would touch mp3 FLAC only 😂

@VRchitecture Год назад

@@alexschoenfelder-lopez4374 32bit/384kHz min or keep it to yourself 😒

@VRchitecture Год назад

I think most audiophiles just pretend they hear the difference between 100$ and 1000$ audio cable, even if they don’t hear or know for sure there isn’t. People really like the idea of belonging to the elite, so no other audiophile would destroy this illusion, or they all would draw themselves as pretentious liars at best or fools who spent insane amount of grands on something practically useless at worst. You need to train your ears and brain for a loooong time in order be able to analyze what you hear. This isn’t a skill you obtain passively listening music. After certain threshold even the best audio engineer in the world wouldn’t notice difference in “quality” or whatever. Not to mention that the older you get the narrower your hearing range becomes (especially it’s upper threshold)

@mspysu79 5 лет назад

A nice simple explanation of a very complicated topic. The video storage method you speak of at the end is the Sony PCM-1630 format and it was used on both U-Matic and 1" C format videotape, there was a consumer version the PCM-F1 that was normally used with Betamax VCR's (although any analog video recorder would work).

@adam872 2 года назад

I've worked with those devices before. I thought it was cool at the time to think that you could store digital audio on a video cassette and then of course ADAT came along to do multi-track.

@stephenZX 5 лет назад

Wiggly Wobblies....go easy with those technical terms, some of us are still new to this :)

@macronencer 4 года назад

I learned a few things from this, despite being very interested in this stuff already. Thanks, great video! And here's a little fact for you, which I came up with decades ago: If you were to record a band's live performance lasting about 1 hour and 40 minutes (which seems plausible) in CD quality stereo, uncompressed, then you'd need... 1 gigabyte! 1 "gig" of data, to store a gig. Hee hee!

@doruchiriac606 Год назад

RU-vid randomly recommended this video to me this morning, even though I already watched it some time ago, and I decided to see it again. After that, today I had a course in digital electronics (I'm a student in Computer Science) and, no joke, basically everything I was told in the course was contained in this video; my teacher was amazed I knew what the Nyquist-Shannon theorem stated 😂😂😂

@JoshBreakdowns 9 месяцев назад

Some folks may be surprised to learn that the Nyquist-Shannon sampling theorem is also extremely relevant in the field of astrophotography. And for the same reason: it is the digital representation of an analog signal. Amazing how their work in the 1920's is still massive relevant over 100 years later.

@KarldorisLambley 9 месяцев назад

i watched this video a year ago. it was all Greek, im afraid. However, after a year in which Ive bought oodles of components, and ICs, an oscilloscope, a function generator, and a soldering iron, then watched all the electro-boom videos again and again, i now get 90% of the video. comprehending a previously incomprehensible thing is the most fantastic feeling. cheers.

@jwproductions5070 5 лет назад

I was just waiting for another video of yours; I'm glad it's here.

@82abn34 4 года назад

A beautiful explanation. I can't imagine how you struggled to achieve such an elegant and balanced presentation without mathematics. Thanks! Ive been thinking about this topic for years and today you've helped me reach that very important intuitive feel.

@jimmy21584 4 года назад

Nyquist Shannon Theorem would have to be the single most valuable piece of knowledge to do with digital signal processing. So handy to be able to answer a customer re. how much bandwidth to allow for a signal: “yes, I am sure that is the bandwidth needed. No, the signal will be perfect. Yes. Literally perfect.”

@Seraph.G 5 лет назад

You have some of the most in-depth content on these topics I've found on RU-vid and I've learned so much from your channel!

@joshsampey2460 3 года назад

You are officially the first channel I have supported on patreon. Every video is informative, free of gimmicks, well written with great nerd humor thrown in.

@theclangers8567 Год назад

Same here. Just did it.

@josephlucas502 5 лет назад

This video is awesome! I love your explanation of Nyquist-Shannon. It's the first time I've heard it explained well. Plus all your videos are amazing.

@AndreiVassiliev 5 лет назад

This channel is amazing. The way everything is explained is so clear. Seriously excellent content!

@ManikSethisuwan 4 года назад

What a beautiful background cabinet. I can see a lot of love and care went into it.

@NickInTimeFilms 5 лет назад

Welp, this one finally did it, subscriber I now am. This video was excellent and so far up my ally it's almost uncanny. The visuals and concise descriptions of 15 minutes just taught me more then 2+ weeks of random internet research and has really brought an understanding to it all. The band limit on the input AND output is what really brought it home, as did the descriptions of "infinite" frequency transitions causing strange looking recreations. So thank you so much for all you've done.

@sebastianelytron8450 5 лет назад

Someone explain to me how this guy can't hit 200K when Linus Tech Tips is approaching 7 million?

@asdkant 5 лет назад

Best explained by CGP Grey: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-rE3j_RHkqJc.html

@asdkant 5 лет назад

Also, different audience (not *that* many people are interested in this kind of stuff)

@xldkxnewyorker8914 5 лет назад

Lack of RGB.

@sGnNPlayer 5 лет назад

People just want to be entertained whilst shutting their brain off. They don't get that understanding things can be entertaining too.

@Muonium1 5 лет назад

*MOLECULAR FOOD SCANNERS*

@robincross4625 2 года назад

Retired NPR Stations Chief Engineer here. Everything you stated is exactly true. In the real world many times there are no low-pass filters before the ADC. We usually recorded our Masters at 48K/96.

@stephenbott4470 8 месяцев назад

I've been teaching Music Tech for several years, and yours was the clearest representation of A/D conversion I've seen yet!

@KairuHakubi 4 года назад

oh my god, i think I actually get this the dots represent the segments between curves that follow particular shape rules, so that's all you need to store. It's like a compression algorithm built into the geometry of sound...?

@dlarge6502 4 года назад

Yes. The samples are simply snapshots of a point on a waveform in a small fraction of time. Mathematically, the only possible waveform that can pass through all those sample points is the original waveform. Thus the samples recreate the exact waveform that was sampled. Nyquist states that to reproduce the exact waveform you must have at least 2 sample points between a peak and a trough. Thus you must sample at twice the frequency you wish to be your upper limit. So CD is 44,100 samples a second to perfectly recreate frequencies below 22,050 Hz.

@fffUUUUUU 5 лет назад

Thanks for another great tech deep-dive video. Please consider another video explaining SACD 1-bit PWM audio encoding system. It's almost not covered among audio-tech enthusiasts...

@C.I... 5 лет назад

It took me days to get my head around that. The fact that it's recursive means there's no easy starting point - every loop needs the previous looped steps to have happened for there to be any data to make sense of/learn about.

@nickwallette6201 5 лет назад

Not really. In as much as you can't have a waveform without multiple samples, yes. But, the effect of past samples diminishes greatly in a short time due to the band limiting again. Instead of multiple vertical steps, as in the (PCM) examples in this video, DSD or PWM (same thing, different marketing) just oscillate from the extreme top and bottom values at a much much higher rate. Instead of 65536 vertical steps at 44kHz, there are only two steps but at a couple MHz.

@C.I... 5 лет назад

That's one of the steps in the simpler form of PWM. Omitting lots, the error between this 0 or 1 is constantly fed back into the input to give a correct average over time (essentially making the 0s and 1s "down" or "up" commands for the drawing of the waveform). It's not as simple as just increasing the sample rate and decreasing the bit depth. I studied this stuff.

@nickwallette6201 5 лет назад

I think you're thinking of Delta-Sigma modulation, which uses successive approximation to achieve the result of a resistor ladder without the requirement of super high precision resistors. PWM doesn't have or need a feedback signal. The duty cycle determines the output. Whatever is encoded in the bitstream gets transmitted as-is and low-passed. You can actually make a DSD "DAC" with a push-pull TTL output, and an RC filter. Now if you're talking about the encoding process, then yes - you need an oscillator, a comparator (too high? too low?), and a feedback from after the filter as an input to the comp. I study this stuff too. ;-)

@C.I... 5 лет назад

Yes I was - you're right.

@JimBob1937 5 лет назад

An excellent overview. You have a skill for simplifying such topics, which isn't easy.

@fmphotooffice5513 4 года назад

Home run. Excellent presentation. IMO one of your best edited text to digital video conversions.

@solhsa 5 лет назад

This is the best representation of the material I've seen, and would have been very useful back when I was in school studying this stuff.

@andrewgc19881 5 лет назад

I really wish Monty would make more videos - he really had a great understanding of the topic and a excellent teacher.

@ceber54 5 лет назад

This is the best introduction to the Nyquist-Shannon theorem that i've ever seen, with almost no mathematics implied. When i saw that theorem the first time at the college, i really realize that say that an analog record media is better than a digital one, at least for the CDs, it's a total fallacy. I learned it in class of adquisition and signals processing a few years ago. Pd. I'm physicist.

@Eletronicafg 5 лет назад

Excellent video! I love your way of explaining things accurately, in a accessible way and without dumbing it down.

@Myrtone 5 лет назад

Regarding 4:51-5:09, I have explained this before and will say it again; The sample value going between the highest and lowest possible values at half the sample rate can only represent a sinewave at one phase or exactly the opposite phase. Two samples per cycle are not enough because of the possibility of phase mismatches, and these are even quite likely. If those two samples fall on zero crossing points, the waveform cannot hit them at all. The sampling rate needs to be greater than twice the highest frequency of a baseband signal to avoid phase mismatches, and there is never a need for a "perfect" filter.

@chitlitlah Год назад

Yeah, as I understand it, the sample rate only needs to be very slightly above double the frequency limit, but it can't be exactly double. It's an exclusive minimum.

@ZeroStatic Год назад

Please remember that the sample rate on a CD is 44100 and the filter cuts all frequencies above 20Khz. The sample rate is actually well above the nyquist rate and so any sine wave that passes the filter has its phase relationship preserved.

@SyphistPrime 5 лет назад

I thought it created audio that was choppy but sampled fast enough to be indistinguishable. It's interesting to know that the low pass filter smooths it out and that it's truly lossless.

@dlarge6502 5 лет назад

It makes you realise that many CD's that sound bad sound bad because they are perfectly reproducing a bad recording and not because they are cd's. Then you see that the so called "hi-res" music (which isnt needed as cd audio is designed to be perfect anyway) sounds better because they used a better quality recording. So why are us consumers being messed with when buying cd's?

@nbuuck 5 лет назад

I greatly appreciate the level of detail you achieve in your videos. RU-vid is somewhat typecast by videos that are extremely topical and high level - one doesn't really learn anything from so many of the technology channels on this platform. Your channel, on the other hand, has never failed to teach me something new and often valuable with each video of the couple dozen I've watched. Thank you.

@nox_machina 4 года назад

I've recently discovered the channel and I'm essentially binge watching the content because it's awesome!

@sergiyradonezhsky634 4 года назад

I'll tell you what man, the quality of your content is just simply top notch. idk if you do all this by yourself, but seriously good job. been following your channel for a while and you know sometimes I find myself binge watching some of the older stuff just a little too often, but again that only just helps stress what I've previously stated; you, my friend do an excellent job! keep it up!

@NovemberBegin 5 лет назад

An excellent explanation of this phenomenon, at different levels of expertise to boot. This guy needs a wider audience. +1 sub for you sir

@FindLiberty 5 лет назад

Yep

@Paticula1135 5 лет назад

I've been watching your videos for a while and been impressed with the mix of entertainment and information. But then I saw this one and man I was just blown away. I've worked with Fourier Transforms before in my university physics studies and I deeply admire the way you go through, essentially, an application of it in such detail but without it ever becoming overwhelming! Heck, I'll readily admit that I didn't even think about how the audio signal, post-digital-conversion, would, essentially, be transformed back into its original form, but when you put it like you do, it's so obvious and simple! And your, admittedly brief, but still very precise explanation of the electronics of the DAC was excellent as well. I can only say that I hope you continue making videos as excellent as this one, because right now I can honestly say you offer probably some of the best content on RU-vid I've seen!

@alexvartanian464 5 лет назад

I love your videos. I am a traveling it tech. Every time I get assigned to a new client you out out another video for the last year we have been in sync. Each one of your videos over the last year represents another client I have worked with. Thtas incredible. Keep up the good work

@michelesignorini2685 5 лет назад

awesome video! i wasn't aware of the LPF in the DAC and i always thought it was like a square wave caused by digital processing, but it isn't. MINDBLOWING!!!

@bfish89ryuhayabusa 5 лет назад

I appreciate that the audacity waveform we saw was the audio we were hearing at the moment.

@tomstern1681 5 лет назад

This is possibly the best video about sampling on RU-vid right now. Good job sir!

@catsspat 5 лет назад

This reminded me of a paper I read many years ago about quantization and dithering. It explained it in a way that even a child could understand. Draw a fairly large letter (say an A) on a piece of paper, but make sure it's small enough to completely cover with your hand. Then cover it with your hand, under your fingers. Spread out the fingers just a little, so you can see there are lines there, but not so wide that you can read the character. Now, slide your hand up and down on the paper while keeping the shape of your hand the same. You can now see the whole letter. It's blurry (noisy) under your moving fingers, but you can see the whole letter, whereas before you started sliding your hand up and down, it was clear (a few lines), but you couldn't see the whole letter. Not super scientific, but I think it's a good description of the process to get kids interested in the stuff.

@GoldSrc_ 5 лет назад

Ah yes, Monty's video made me realize how wrong I was about digital audio years ago, that video is truly a MUST watch.

@thedanyesful 4 года назад

Thank you for this great video.

@HeadCodeMonkey82 4 года назад

You are a great presenter / educator, and I love the depth you go into in a topic.

@Braeden123698745 5 лет назад

I want to high five you so hard, bringing math into the crazy world of audio. Audio is purely subjective, but now you've brought a tool in to show that digital is just as good.

@CatsMeowPaw 5 лет назад

I'm just waiting for the Golden Ear brigade to hit the comments. 'But I have special hearing that goes way beyond 20Khz! (no you don't)' 'I can "feel" the music better with an infinitely accurate analog signal (no you can't)' 'Digital doesn't capture all the "nuances" of music (yes it does)'

@quayzar1 5 лет назад

I think people that like vinyl for everything just don't know what they're talking about, are comparing vinyl to mp3, or have terrible DACs.

@jfbaquero 5 лет назад

I am audiophile and agree with the above, the thing is that machines are not perfect and you need great engineering to make this work well. I am a fan of CDs because they got it right from the beginning using math and the physics. LPs are cool and effortless to reproduce but have lots of flaws. A turntable is a "simple" machine, a CD player/DAC are pretty complex ones. So the difference in reproduction is in the equipment not in the theory and there is a big difference between consumer audio gear and high fi gear.

@5thDragonDreamCaster 5 лет назад

Some people can hear up to 24KHz, but only people who haven't abused their hearing AND that are under the age of 24. This extra range doesn't contribute much to the overall sound though, and most people able to hear this tiny bit of extra frequencies don't care about good music anyway.

@WFNKcom 5 лет назад

are you saying that you only detect sound through your ears?

@MisterHavoc 5 лет назад

Some people CAN hear past 20 kHz, as it's only the human average, not a set-in-stone value. I'm one of those freaks who can hear some of it, like when some kinds of electronics are running. Nearly broke a window because of it. My ex had left some kind of air-filter/ionizer... thing in my closet when she moved out. I pulled it out to see if it worked. Plugged it in, turned it on while holding it (worst mistake ever...), and it started making one of the highest frequency noises I've ever heard. I literally threw it across the room, yanking the cord out of the socket and almost out a window. It was awful. And no, being able to hear those higher frequencies doesn't add anything to the "music experience." All the really high frequency stuff just gets drowned out 99.9% of the time. You're seriously not missing out on anything if your hearing doesn't go outside the average range, other than the occasional headache because you can hear some tiny, awful tone/sound from a coworkers' computer that literally no one else in the office can hear.

@AusSkiller 5 лет назад

This is why I've always hated people who claim records are better than digital, if they prefer the inferior sound of a record that's fine, but they could just hook the output of a record player up to a digital recorder and save that, then when they play back the digital recording and it will sound exactly like the record with all it's flaws included. That's also why the "records sound the way the artist intended" argument is so bullshit, if they really wanted their songs to sound like it does when played from a record then they would use a record to make the digital recordings.

@Myrtone 5 лет назад

I think they are referring to the best quality records (in mint condition), played on high end equipment.

@AusSkiller 5 лет назад

But it would still be inferior to a digital recording played back on the same equipment. Even if you had an absolutely perfect never before played record, it would only match the quality of a digital recording on the first play, the second playback would be objectively worse from the wear of the first playback, even with an optical/laser turntable in a vacuum there would be eventual wear and degradation of the record over time. Some people might prefer the sound of a record, which again is perfectly fine, I have no doubt a lot of people do and they are not wrong for preferring it, but there is no real objective benefit to a record over digital, digital is superior in just about every way.

@Myrtone 5 лет назад

A digital recording cannot be played back on the exact same equipment as an analog medium. In order to really compare analog a digital, what is needed is comparison of an analog and a digital recording similar in dynamic range, frequency response, etc.

@nickp1987 5 лет назад

I like and buy vinyl. But it's because I appreciate them as art objects and enjoy sort of the ceremony of Putting On and Listening to a Record. I, of course, also buy CD's for the same reason and the high quality sound. :P

@davidmckean955 5 лет назад

Records tend to sound better than CDs overall because mastering was better in the days of vinyl. And they do sound the way that the artist intended because the artists approved the master. That's not necessarily true of the catalog CD that was released decades after. But there's no technical limitation keeping CDs from sounding as good, it's just that most of the time they don't. Of course not all of this is true if you only listen to newer music so your experience may be different than mine.

@Pentamicle 5 лет назад

Thank you for this, the square wave example in particular was something o have been struggling with nobody else seemed to explain anywhere.

@yuzhang2755 Год назад

Great work! Every person who wants to talk about digital audio should watch this first and understand it 100%. There are too many youtubers talking about digital audio without understanding the "backbone" of it and all they do is to spread misinformation.

@McIntec 4 года назад

I've seen that video from Xiph.org before. It has excellent information.Thanks for referencing it.

@RCAvhstape 5 лет назад

I studied this stuff in college, and I must say this a great explanation of it, your motion diagrams regarding the Fourier series and aliasing were very informative. I've never gotten into the habit of arguing with audiophiles; it's rather like arguing with flat earthers or other such nuts who refuse to listen to logic, but it's good to be able to explain this stuff to those who are willing.

@kylethedford 5 лет назад

This is the most mind blowing thing I've learned about audio yet! Keep up the good work!

@joaomarcelobadu 4 года назад

Thank you very much for this awesome video! This is something I was curious about for decades.

@smallmoneysalvia 5 лет назад

Nice choice with the ds1054z! Glad to see you finally took the plunge

@smallmoneysalvia 5 лет назад

Yeah by far, but 100mhz is only single channel, if you go to 2 channels it drops to 50mhz, and 3 or 4 goes to 25mhz.

@douglasquaid1418 5 лет назад

soupisgdfood that is not true

@smallmoneysalvia 5 лет назад

Douglas Quaid I was wrong. You DO lose bandwidth due to reduced sample rate with each new opened channel, except when going from 3 to 4 channels, bit it’s due to lost resolution only. Though, that all being said, the minimum sample rate is 250Msamples/sec, which theoretically can do 100mhz but you’re really cutting it close there.

@douglasquaid1418 5 лет назад

You are 100% false. The sample rate drops, not the bandwidth. 1 channel 1GS/s 2 channels 500MS/s 250MS/s on 3channels...

@smallmoneysalvia 5 лет назад

Douglas...Quaid...check...the...edit................................

@justpaul899 5 лет назад

Great job explaining the square wave form issue! I still prefer analog audio, but at least now I can't use the "stair stepping" argument anymore :)

@KaosFireMaker 4 года назад

Its perfectly fine to prefer the analogue stuff. While it may be objectively less identical to the original recording, that doesn't make it worse, in the same way a painting is no worse nor better than a photo.

@Chillingworth 2 года назад

My mind was blown at 14:58 when you drew that curve so well

@nickcarter4006 5 лет назад

This is the best explanation of these concepts I’ve ever seen, including my college classes. Kudos and thanks!

@marcan42 5 лет назад

Just want to add that the stairstep output + lowpass combination isn't quite how proper DACs work. The lowpass part is fine, but the stairstep method itself (zero-order hold) does not have a flat frequency response below the Nyquist limit, it actually drops to 0 as you get there. Real DACs use a combination of tricks. For example, if instead of having a stairstep that goes from sample to sample, you have 1/2 sample width "bars" at each sample, with the signal dropping back to 0 volts for half of each sample, then the high frequency response is more gradual, going to 0 at twice the Nyquist frequency. There is still some loss in the audible range that you care about, but then you can compensate it with a digital filter before the DAC (often part of DAC chips themselves). If instead of spitting out an on-off pattern directly like that you create it digitally (by doubling the sampling rate and having zeros between samples), then add a digital filter, you've just created an oversampling DAC which is even more effective. Here's a nice PDF from TI that shows the various approaches: training.ti.com/sites/default/files/docs/TIPL4705%20-%20DAC%20Output%20Response.pdf But really, the important takeaway is that we understand all of this and we can engineer real DACs to be pretty much perfect as far as our hearing can tell. Correction: I'm off by a factor of two about the response. Sample and hold drops to 0 at the sampling frequency (twice the Nyquist limit) and the 1/2 width method drop to 0 at twice the sampling frequency.

@Alexagrigorieff 5 лет назад

Yes, that's what I said in my earlier comment. Basically, if you have stair-step signal, you get about -3 dB loss at 20 kHz. With 2x oversample, the loss will be -0.75 dB, and with 4x, it's -0.18 dB. Coincidentally, an effect on the frequency response of using 50% duty cycle bars will be the same as 2x oversample, and with 25% duty cycle it's same as 4x oversample. With true oversample, though, you'll just get the aliases farther in frequency, so you can use a simpler analog filter.

@Alexagrigorieff 5 лет назад

Correction: with stairstep signal, the frequency response at near Nyquist frequency goes to 2/π, not to 0.

@marcan42 5 лет назад

Ah, yes, I was off by a factor of two. It goes to 0 at the sampling frequency (which makes sense) and at half that you get 2/π, which is -3.9dB or so. And yeah, the point of oversampling is to get rid of the aliasing within the new wider response digitally, so then the analog filter is much easier to make.

@jackwright7014 5 лет назад

Brilliant informative video. I learn so much! I knew that the theorem allows perfect replication of analog audio digitally, which is why it bugs me when people say they hear a quality difference between CD and high-res audio. Which is true if you want to hear an orchestra at real-life volume and then a mouse squeaking straight after.

@Myrtone 2 года назад

Except that digital audio is not just sampled, it is quantised.

@richardiredale3128 2 года назад

@@Myrtone Sampling is for frequency response, quantising does noise level. 16 bits does a very, very, very low noise level, I recall somethling like 85+db, and dithering drops that much further. Way beyond what you can discern in a typical listening environment.

@charleswiltshire 5 лет назад

I always wondered about this but now I understand the filter is key - and just when I was questioning how ADC's work, out popped the answer. Very cool video indeed thank you - Technology Connections is fast becoming my favourite RU-vid channel.

@romyaz1713 5 лет назад

I tip my hat to you, sir. This is one of the most concise and elegant explanations of the digital sampling process for a non-engineer that I have ever seen. You've elegantly avoided talking about a reconstruction kernel, but at the same time put a stop to the never-ending digital-analog audio wars. Thank you!

@justanotheryoutubechannel 5 лет назад

Holy crap, that’s crazy! Why do audiophiles hate digital sound so much if it sounds perfect in the end?

@VideoArchiveGuy 5 лет назад

Because you are dealing with theoretical vs. practice. It's easy to say "the low pass filter..." but low pass filters aren't perfect. Early brick wall filters rang horribly, causing artifacts to the audio as it limited it. Even today they're not perfect. Then DACs are also not perfect. It's nearly impossible to design ladder DACs these days because resistors have variances and they cannot be trimmed to an accuracy where even the two channels in a stereo DAC provide the exact same output per mono channel fed into either channel. Modern single bit DACS have their own issues, and finally, there's that filter problem again. There are also a variety of other issues, but these are some of the easier to explain ones.

@jhutt8002 Год назад

There also the truth that while analog audio has much more errors and smearing than in digital realm, those "problems" can sound comfortable and even really good. That's why analog recorded albums sound (subjectively) better and why people love vinyl even today. Guitars are perfect example of this. Electric guitars get their traditionally distinctive soundscape from poorly designed amplifier circuits, sometimes enhanced by pushing them too far to create walls of analog distortion.

@Lemon_Inspector Год назад

Because nobody makes solid-gold transistors.

@distortingjack Год назад

@@VideoArchiveGuy Digital low-pass filters are actually perfect, within the limitations of what a real-life oscillation is. The ringing of a very steep low-pass filter is concentrated at the knee frequency, meaning it would be at 20 kHz or above for 44.1 kHz. There are three reasons why digital can be abhorred by "audiophiles". The first one is that these low-pass filters were originally done in analogue, and that caused analogue ratty distortion on the top end of a signal. Nowadays converters don't work the same way at all. They capture a very high frequency range, way outside the limit of hearing, and then apply a digital filter that doesn't cause that distortion. The second one is that a lot of people have absolutely no idea about the info in this video. I have heard the "stairstep", the "ultrasonic info", and the "minimum timing information" myths from people who really, really should have known better amongst sound engineers; the average Joe would fare way worse. The third one is that music often sounds pretty cool with the added distortions of tape, vinyl, and extra analogue stages. A lot of that distortion sounds nice! Even today, most pop music recordings have distortion added to them because, well, it sounds better that way. People would be shocked at the amount of distortion, either digital or analogue, added to almost every pop and rock album even today. However, if it sounds better to add more distortion at the playback stage, it means that maybe the producers and engineers should have added it at the production stage. But that's just a preference. The absolute proof that digital is a better medium than vinyl is that you can record a digital signal into vinyl and it will sound like vinyl. However, you can record a vinyl signal into digital, and it will sound *exactly* like the vinyl.

@VideoArchiveGuy Год назад

@@distortingjack Digitally sourced vinyl still usually sounds like digital. It is true that vinyl recorded to digital will retain character of the vinyl, with many listeners preferring the sound of a digital recording sourced from a good LP to that released as a digital recording.

@Lucarios111 5 лет назад

I love the F1 in the background

@couchetard1984 4 года назад

Well done! Very difficult teaching job, executed beautifully. I need to watch it again to understand whether the output contains extrapolated data or not. But the magic of the low pass filter has me hooked. Love all your work. One day I'll have Patreon money, which you totally deserve.

@timmckeand7631 5 лет назад

This is the best video you've done . Which is saying a lot!!

@zingaman 5 лет назад

WOW.. I did not know that Umatic was used to store early digital audio! Who knew?? Thanks!

@marktubeie07 5 лет назад

Indeed - professionally back in the day we used U-matic to master audio albums digitally and run analogue copies from that!

@gplustree 5 лет назад

Yeah, was super cool to finally learn the origin of the weird 44.1 rate

@PJL3791 5 лет назад

Sounds like the reverse of how the ZX Spectrum computer loaded data from a program stored on cassettes, which created sounds similar to dial-up internet that produced raster bars on the screen.

@misterhat5823 5 лет назад

Yep. Few know that it's the reason for 44.1kHz.

@BertGrink 5 лет назад

Yeah that blew my mind as well ;)

@pokepress 5 лет назад

Just out of curiosity, is there some sort of theoretical limit to the highest frequency sound that can be carried by air itself? It probably varies based on pressure and such, but I was curious.

@anothergol 5 лет назад

interesting question. Google says 5GHz?

@HalfgildWynac 5 лет назад

That is about right. The mean distance a molecule travels between collisions can be estimated as 50-100 nanometers. With the speed of sound of 340 m/s you can get your limit. If the wavelength is smaller than what a molecule runs between collisions, you can expect the regions of high and low pressure become extremely ill-defined. It gives you a limit of about 2 to 5 GHz. This is an estimate, of course. I imagine the signal becomes too noisy and attenuates too fast way before you reach this limit. (the estimate is specifically for air at room temperature and the pressure of 1 atmosphere; solids work differently and transfer sound faster)

@kurt0kasem 4 года назад

Thank you so much. I am currently writing a audio modem in python from ground up. I had much theoretical knowledge about those mathematics and processing techniques, but had never REALLY UNDERSTOOD IT. Thanks to your video I do now. Thank you so much. Please keep on bringing those videos

@ErinIsBlueBlue Год назад

I really enjoyed this video. Thank you James.

@pokepress 5 лет назад

Some of the concepts here might be easier to demonstrate in audio form if you used some lower sample rate files (say at 8000 or 11025 samples per second), so that the reproducible frequency limit is within the range of normal hearing.

@LanceMabu 5 лет назад

I'm gonna adjust my glasses and wag my finger while saying that the cutoff frequency of a filter is measured when the output has changed 3dB. I also need to say that you make awesome videos that keeps me entertained and informed.

@lawrencedoliveiro9104 5 лет назад

That’s an analog definition. And what about higher-order filters?

@LanceMabu 5 лет назад

He was also talking about an analog filter and as far as I remember it's a definition for all filters but it's been about 16 years since I finished my education in electronics en.wikipedia.org/wiki/Cutoff_frequency

@lawrencedoliveiro9104 5 лет назад

Digital filters are quite capable of implementing a “brick wall” cutoff.

@allstar930 4 года назад

This is so good. You do such a great job explaining these confusing topics.

@ryanb9873 5 лет назад

FANTASTIC explanation, even without any mention of polynomials, etc. Great job.

@ianmsutherland 5 лет назад

I really have no idea what 90% of this means, but I know I like it.

@koonoho 5 лет назад

the sampling frequency has to be bigger then two times the highest frequency contained in the signal and not bigger or equal. imagine measuring sin(wt) and sampling it at exactly twice it's frequency, and the timing of the samples exactly so that each sample is taken when the signal is 0. how do you know the signal is sin(wt) instead of -sin(wt) or just 0? that's why the sampling frequency has to be higher then two times the highest signal frequency.

@Myrtone 5 лет назад

Exactly, considering what would happen if the sampling rate is exactly twice the frequency and the timing of the samples is not taken when the signal is at the peak voltage, this has escaped Alec's attention.

@anothergol 5 лет назад

It can normally be exactly twice, only you won't have phase information at exactly Nyquist

@Myrtone 5 лет назад

Even at "exactly Nyquist" the amplitude information also isn't meaningful, since the sampling phase will affect sample values. Finally, samples at zero crossing points will mean no signal at all, that is "mid-mid-mid" not "low-high-low".

@Liam-qr7zn 4 года назад

This is true, but it's of more interest to mathematicians than engineers, since an engineer will never encounter a wave at the exact frequency cut-off of the low-pass filter.

@Hermiel 4 года назад

I've been evangelizing Monty Montgomery's video in RU-vid comments for years, leaving a friendly note and a link every time I come across a video misrepresenting the science. This video is an excellent supplement to that one; I really like your explanation of how in the physical world everything is naturally band-limited because of mass and the extents of hearing and so forth. I will definitely be sharing this as I continue my crusade to spread the digital audio gospel. KUDOS!