Nyquist-Shannon; The Backbone of Digital Sound technology connections

by noithatSDFGH



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Nyquist-Shannon; The Backbone of Digital Sound

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48 comments

Teo Trunk 21/10/2021 - 1:43 AM

Great content!

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Mackinstyle 21/10/2021 - 1:43 AM

So does this mean that the extra CPU cost of my emulator outputting at 48khz is entirely pointless?

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Mackinstyle 21/10/2021 - 1:43 AM

Okay I think something just clicked for me when you talked about how sound works in nature. I understood all that, but I never really pieced it together. All sounds in nature ARE a summation of sine waves, given that sine waves form when things vibrate. And this is what make fourier transforms far more accurate than just a clever optimization hack. There is no such thing as a perfect square wave or sawtooth wave, etc. in nature. Nothing can ever produce that.

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Hapa Siuhengalu 21/10/2021 - 1:43 AM

I know this video is 3 years old now, but what about higher sample rates?

My audio interface at home does 48KHz, and my DAW supports up to 96KHz, but I only ever moved up from 44.1KHz because when collaborating with other producers, they demanded the highest sample rate I could provide them

I can also definitely “feel” a difference between different sample rates, if that makes sense

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John Roehsler 21/10/2021 - 1:43 AM

Another excellent video.

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Smile 21/10/2021 - 1:43 AM

44.1kHz is also the product of the squares of the first 4 prime numbers:)

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Larry Troxler 21/10/2021 - 1:43 AM

This is not accurate. The sampling rate has to be more than twice than twice the highest frequency not just equal to it. Consider the the case where you have a sine wave, and a sampling rate twice the frequency of the sine wave. So the sine wave will be sampled twice per cycle. Well what happens if be chance the samples are catching the zero crossings? Then there is zero information about the input signal, because every sample will be the same value.

Also, you mentioned the low pass filter to reconstruct the analog signal in the DAC. But you neglected to mention that not all low pass filters are the same (for example, butterworth vs. Chebyshev). The low pass filter to reconstruct the original has to have a very specific frequency response. If anyone wants to know more details, email me or post here.

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jeice13 21/10/2021 - 1:43 AM

Wouldnt it be difficult to create frequencies slightly lower than the limit unless you can lower the sampling rate?

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Simon Schalbers 21/10/2021 - 1:43 AM

Being honest here
I had to check if I was subscribed despite watching all videos of the last 2 years.
I am though, which is good

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dontaskiwasbored2008 21/10/2021 - 1:43 AM

This digital audio series is great! Thank you! The Monty video was excellent as well. Too bad they have comments disabled over there.

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Chuu Ni 21/10/2021 - 1:43 AM

What I don't get about Shannon-Nyquist is what happens when you try to generate a 22049.9999 Hz signal. It is within the band-limit, so it should work, but because of the discrete sampling you basically get hundreds of thousands of samples that are basically silent. I can't see how this can be reproduced as anything but a very slowly modulated 22050 Hz output. I get that in the perfect mathematical reality where all the samples are known, the only bandlimited signal that can result from this is the input 22049.9999 Hz signal, but the speakers (or more likely at that frequency, oscilloscope) doesn't know about the samples significantly away from zero for many, many seconds.

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Mitty Patrick 21/10/2021 - 1:43 AM

I just checked what I could percieve. I'm 24 and the highest I can hear is 18,887Hz.

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Jenn W 21/10/2021 - 1:43 AM

I was in a Master's program in Electro Acoustic Music at Dartmouth College in 1990. I studied with Jon Appleton, the designer of the Synclavier. We had a "tapeless studio" which recorded 8 tracks for 15 minutes (not configurable) and it took up an entire rack. Anyway, I believed so fiercely in the inferiority of digital audio (largely due to my former teacher's opinions on it) that I did an experiment in Acoustics class to prove you could hear the digital artifacts. I could not prove it, and at the time I believed it's because of the limitations of my experimental design. I'm a little surprised nobody taught me about Nyquist-Shannon. Like, especially since my acoustics teacher helped me design the experiment.

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ivarwind 21/10/2021 - 1:43 AM

Only problem is, it's trivial to show that the same (simple analogue sine wave for a finite or infinite amount of time) signal can give two (in fact "infinitely" – limited by bit depth – many) digital signals at twice the sampling frequency ranging from completely flat to full amplitude. This is the very-easy-to-understand case, and is already covered by adding a strict inequality to the N-S theorem. It gets trickier (but not much) with frequencies below but close to the Nyquist limit (i.e.down to perhaps a quarter of the frequency) – it's still easy to understand, but mathematically sub-Nyquist artefacts are trickier – so much so, that researchers while aware of them, tend to ignore them.
Fortunately CDs are sampled at 44,1 KHz, and once we get down to frequencies that people who obsess over these things can hear, the corresponding beat tones are already getting close to the actual frequency.
(Of course this doesn't mean there's anything wrong with the Nyquist-Shannon theorem, only that – as is so often the case when applying mathematical theorems to physical systems – people may fail to take the limitations of the theorem into account – or maybe more accurately the limitations of the real world – which sometimes makes no practical difference, and sometimes makes all the difference!)

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David Eldridge 21/10/2021 - 1:43 AM

That CD "down to the Moon by Andreas Vollenweider was the first CD I ever owned. I got it for Christmas with my first CD player. Weird

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Paolo Carlet 21/10/2021 - 1:43 AM

For those who speaks Italian here there's a milestone of Nyquist-Shannon demonstrations
https://youtu.be/EOR8Uz27s3Y

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Leopold5100 21/10/2021 - 1:43 AM

WOW well done

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Ion Busman 21/10/2021 - 1:43 AM

So if a digital signal is just a 0 or 1 no matter of amplitude… how does digital audio work? Where there is clear points needed in between? By looking at the analog signal

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Alexander Gaukin 21/10/2021 - 1:43 AM

I am a telecom engineer, and Shannon-Nyqist is more than familiar to me. However, I found some interesting insights in your video.

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John Mayer 21/10/2021 - 1:43 AM

the overshoot. the overshoot and ring are the missing piece.

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T0biasCZe 21/10/2021 - 1:43 AM

74 ? they are 80 minutes long, and with overburn you can put 82minutes on them
and they are 90 minute cds

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Chillingworth 21/10/2021 - 1:43 AM

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

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gammerbro567 21/10/2021 - 1:43 AM

What I’m getting from this is that while math is cool, low pass filters are magic.

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ShotecMusic 21/10/2021 - 1:43 AM

I need a professional to help me stop all of my imaginary conversations and fights about analog vs. digital audio…….. but maybe I'm just getting myself prepared if it happens in real 😀

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Matt Johnson 21/10/2021 - 1:43 AM

You make the same mistake many other people do about the Nyquist theorem. It CANNOT 'perfectly reproduce' audio signals. Some of the formulas involved use infinites which means on paper, in theory, it all works but digital converters that live in the real world cant deal with them so they make approximations which means not a perfect recreation.

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Fishfu 21/10/2021 - 1:43 AM

this was a huge piece of my Electrical Engineering degree. It is a very simple theorem as to almost seem obvious when it's explained, but it has implications all over the place. Not just digital sound.

It's one of my favorites. It is simple and elegant, and I use it regularly despite no longer working directly with digital signals any longer.

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ND Roughrider 21/10/2021 - 1:43 AM

I haven't heard anyone discuss if the filtered or clipped frequencies that we can't hear, have any effect on the lower ones that we can hear. Everyone just assumes if you can't hear it then it's of no use in the reproduction of the recording, but what if it is in fact having an influence on the lower sound waves? Just a thought that I've yet to hear anyone address yet!

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65_roses_jku 21/10/2021 - 1:43 AM

Dude, you lost me

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Kevin Underdown 21/10/2021 - 1:43 AM

Digital audio is merely an approximation.

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J-P Hale 21/10/2021 - 1:43 AM

Awesome work. The visual presentation here is better than the classroom training I had in the ‘90’s when this stuff was mainstream. Great explanation.

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Jeff M 21/10/2021 - 1:43 AM

The R2R ladders have a bandwidth limit as well as do the drivers that drive the resistors of the ladder. So even before a low pass filter some steps will never be square in nature. So yes I agree with this video. ok ok, granted the R2R ladders have pretty good bandwidth most of the time.

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Geoffrey Lydall 21/10/2021 - 1:43 AM

Then there's 1-bit DACs which use PWM and look even worse the jagged 16-bit DACs… but sound the same

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Phillip Wang 21/10/2021 - 1:43 AM

I think you'll get a kick out of this device: https://en.wikipedia.org/wiki/The_Mosquito that takes advantage of high frequency hearing loss by 'older' adults.

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kd1s 21/10/2021 - 1:43 AM

Oh yeah and when Shannon wrote up his paper on Information Theory the bigwigs at Bell Labs knew it would spell the end of the Bell System. And it has.

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James Brown 21/10/2021 - 1:43 AM

I'm curious. What would happen if you omitted the output filter and listened to the output of the DAC directly? Wouldn't human hearing do the same filtering given that we couldn't hear frequencies above 20KHz, or would it introduce artifacts?

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Christoffer Wiig 21/10/2021 - 1:43 AM

I remember being so confused by this as a kid. Had a book that described all sorts tech. When it came to sampling sound waves it was very detailed but missed the part of the signal being band limited. I was confused for weeks on how CDs and adc/dac’s would “know” they picked the right sound.

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ChargedCMOS 21/10/2021 - 1:43 AM

Also, thanks for making the video. Like the lava lamp in the background.

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ChargedCMOS 21/10/2021 - 1:43 AM

Fun fact: the same Nyquist limit is valid on both Ultrasound imaging and MRI imaging since they also deal with frequencies. Thus, there are also aliasing artefacts in both of these methods of imaging if settings are not correct.

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Marc Wolfe 21/10/2021 - 1:43 AM

To connect some dots (ha) for the other nerds out there. It might be easier to think of the filters as limiting slew rate. You can google that term, and see it used in datasheets for OP-amps and MOSFETs, etc.

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Marc Wolfe 21/10/2021 - 1:43 AM

6:05 MORE!

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Marc Wolfe 21/10/2021 - 1:43 AM

5:30 "Everything in nature will oscillates with a sudden impulse of energy." Absolutely. Electrons in an inductor, electrons in a circuit not designed to function as an inductor (parasitic inductance), air going into the intake of an engine, the barrel of a gun from the detonation of the powder, etc.

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Woo Six 21/10/2021 - 1:43 AM

Monty’s video is awesome

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frankgh1 21/10/2021 - 1:43 AM

Vinyl still sounds better through my tube pre stage and tube amp. In my brain anyhow!

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John Barker 21/10/2021 - 1:43 AM

Just try to fit "the Whittaker-Nyquist-Ktelkinov-Shannon Sampling Theorem smoothly into a conversation. It's an accomplishment, like Ogden Edsl Wahalia Blues Ensemble. They proved the theorem that dead puppies aren't much fun. You throw the ball and they don't run.

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eric moeller 21/10/2021 - 1:43 AM

Hell my HT-S100F sony sound bar has no analog input and has a bad audio delay cause it don't want to agree with digital sometimes analog is better but digital has Superior sound quality but they need to work on that delay it also has blue tooth i use it when im cleaning

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eric moeller 21/10/2021 - 1:43 AM

7:53 right mind blown

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mark rigg 21/10/2021 - 1:43 AM

Really well explained and I was really surprised to see the Andreas Vollenweider CD from the 80s which I own.

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klesto92 21/10/2021 - 1:43 AM

Lol two years late but what you describe here is a Fourier Series Expansion, not a Fourier Transformation. They’re different.

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