The intuition behind the Nyquist-Shannon Sampling Theorem

[@oanceatudor4443]

The fact that this guy makes hilarious videos on his other channel and unironically useful videos on this one is impressive

[@thenextboundary834]

What is the other channel?

[@jamesmnguyen]

​@@thenextboundary834 Himself Zach Star

[@giovannicastiglioni4084]

Title should be "Are you able and willing to figure out the original signal?"

[@FireStormOOO_]

That's why we solder the microchips onto the board - can't have them running away when we tell them to do math

[@brendawilliams8062]

@@FireStormOOO_Fourier ✅

[@michaelhall5801]

This upload could not have been timed better. I'm busy learning about this stuff in my signals & systems class and seeing the graphs and plots really helps

[@sensorer]

Nyquist-Shannon theorem is so cool! It lets one connect discrete and continuous signals through their information density, which provides very deep insight. You can also generalize it to signals which do not have compactly supported frequency spectrum like gaussians! And there is a surprising connection to the study of minimal length in quantum mechanics!

[@austinisawesome2066]

I laughed out loud when he said “and this makes sense because of the Fourier transform” cause I thought he was going to dumb it down a bunch. Love how this channel is like a “more mature” math channel where not everything has to be explained at a middle school level. Thanks!

[@prats2834]

I was struggling with this for quite a while but after seeing this video I had my own eureka moment. Thank You for explaining it so clearly I wish everyone had the access to quality education like this.

[@martinoffi9249]

This will help me pass the final exam for my signal processing course tomorrow. Brilliant explanation!

[@johnchessant3012]

this is one of those things that seems simple but is mindbendingly cool. like the 44.1 kHz thing, basically it's saying if we know the signal at these few isolated points, then we know what it is at all times, _unless_ it contains frequencies higher than half of 44.1 kHz, in which case humans can't hear them anyway

[@146fallon]

Thank you so much. I am very grateful that I can understand this theory and why it is periodic in frequency domain. ❤❤❤

[@advaitkamath8442]

Everytime i click on one of these videos, i feel like ive unlocked something magical or divine

[@artemonstrick]

You do this better than profs at my „elite“ university. This makes me sooo mad at our education

[@egor.okhterov]

Because he's focusing on one subject. He doesn't need to do a full course. He can spend a huge amount of time preparing 11 minute video. Professors cannot do that.

[@vlc-cosplayer]

​@@egor.okhterov cope, professors have been teaching the same things for the past 20 years, lmao, don't tell me they haven't figured out a good explanation in all that time If anything, you could make the argument that they're sick of saying the same things over and over (there's a quote about insanity that would fit here), which is why the quality of teaching goes down as time goes on

[@gregorymccoy6797]

I knew all this ...at one time in the past. Nice to see it again. You are the math teacher we never got.

[@nepomukullmann3013]

I wrote a test on this just this afternoon. Great timing and would have loved to have had this before the semester! great video

[@retroforager]

christ all mighty i am so happy you're posting on this channel again!

[@jamesmnguyen]

I've been tackling digital signal processing on my own time and this video really helped solidify my understanding of the Nyquist-Shannon Theorem.

[@WerdFTW]

I'm literally learning about this in one of my classes and we have a midterm next week, so thank you for the good timing, Zach. 🙏

[@ultramohitb]

It’s nice to have a neat visual depiction of how this theorem works. Thanks!

[@fast_gtr]

You made this video exactly while I’m taking an ADC DAC course. Perfect timing!

[@SamuelBelton]

Thank you Zach for such a well presented, detailed and accurate introduction to a difficult concept.

[@soingpeirce]

Bro, I love your videos, this is the first time you've posted one while I was covering it in a class though. We didn't cover the transform part of it, so that really helped me understand WHY aliasing is introduced below double sampling rate

[@楊學翰-m5i]

What a satisfying refresher to Signals and Systems! These topics are really starting to fade away after my graduation

[@HesterClapp]

I've known about this for a while, but now I actually understand it! Thank you so much!

[@idrizpelaj4928]

This is such a wonderful visualization, step by step, and not as abstract as drawing on a whiteboard as most professors do haha. Thank you!

[@KevlarSammy]

You are doing amazing things for the field of EEE. Thank you brilliant!

[@dylanparker130]

Excellent stuff - Sinc Functions, Fourier Transforms, and Aliasing all in 10 minutes. Wow!

[@Frank-ie8dh]

This is the best. Thank you so much.

[@RichardCorongiu]

Thank you thank you...explained to an amateur with a rabid wish to know from first principles. Ive even bought an oscilloscope with FFT to see what a signal looks like without knowing what to look for

[@Lost_S]

incredibly good and simple explanation, thank you

[@adityamaniraja8464]

I have my digital communications exam tomorrow and you posted this video at the right time lol

[@theDreadedBlur]

I am in a class where we apply the Nyquist-Shannon theorem for signal analysis.

[@brian420pm]

Mathematics shedding light into logic, reasoning, assumptions, etc. Well done! 🙏

[@lMINERl]

This comment is sponsered by brilliant. New course that gets you top comment each time

[@chri-k]

it works!

[@nicholas_obert]

Wow

[@michaelrogers1066]

As an electrical engineer that should really be doing my signal processing homework rn, thanks for the video

[@danieljackson89]

This is stunning cheers

[@ProfeARios]

Excellent video. Greetings from Panama 🇵🇦

[@lex6709]

absolutely Love it!

[@aaqilkhan]

Nicely explained. As always!

[@md.adnannabib2066]

I am currently studying this in my course.and just your video

[@das224]

The bit on aliasing is a GREAT visualization =)

[@BiplobHossainSorker]

thanks ❤

[@Saens406]

my favorite theorem of all time

[@agastyasanyal4026]

Omg Zach PLEASE make a convolution video ❤

[@lucykitsune4619]

Damn where were you when I had to learn this shit 7 years ago? Amazing video and really good explanation

[@salarbasiri5959]

best explanation of the subject

[@thanoskarvouniaris6827]

Signals & Systems my favourite course in EE

[@1972hattrick]

Didn’t like DSP?

[@ashwininir9535]

Goat

[@christophkassir1559]

Brilliant!

[@nicolabellemo3054]

why in 5:00 you make copies in the frequency domain of the boxes function?

[@anshuraghav505]

great video

[@zajlord2930]

god damn, why couldnt you make this vid one semester sooner xd

[@galdali10]

You should make more videos like this

[@untodesu]

Actually this repeating of frequency domain can help you to process higher-frequency signals using your regular PC sound card's ADC: sampling essentially acts as a frequency mixer in a heterodyne receiver with a lot more of "collateral" bands. Though I don't really know whether motherboards have a low pass filters on mic inputs or not

[@ColissaPollard]

Hey @zach! This is awesome! May I ask which tools you use to build your graphs and animated visuals?

[@klevisimeri607]

Thanks

[@oskarkrogsgard3014]

Please, make a video about convolution! That would be super helpful!

[@ABZein]

8:23 like Rayleigh criterion in diffraction????

[@yusufserandogmus4118]

Love it

[@DoktorSchaedel]

This brings flashbacks to 3. semester in electrical engineering. Pretty easy stuff as soon as you understand it

[@charlesspringer4709]

"You must sample at a rate twice" the frequency of the signal. Almost right. It must be Greater Than twice, as when you showed the theorem. Sampling at exactly twice will produce a constant or two constants that oscillate. And sampling a little more than twice will take a little less than infinity to determine the frequency. The 44kHz of the audio for music and computer sound cards is more than twice the top range for music but it is well over 100 times the frequency of typical human speech. 250 more than males. For good and timely results using the theorem one must sample at more like 8 or 10 times the frequency of interest and have very good low pass filtering. Sampling at a power of 2 or in sequences a power of 2 long makes computation a lot easier. The more you can "oversample" the better. Good luck, we're all counting on you.

[@hsavietto]

This math is so dense my head Hertz.

[@EvenMoreCheese]

Goatt

[@richardtrager7125]

This gave me ptsd from my Control System course from last semester 💀

[@user24242]

I've always been a little confused about whether 2f is enough, or if strictly greater than 2f is required. At 3:50 you say "faster" and use a greater-than symbol, but at 9:58 you say "at least" while still showing a greater-than. I get that in the real world the sampling frequency is never gonna be exact anyway so you need a decent margin (and you showed CD audio being 44100 not 44k as an example of that), but in theory, can I get away with 2f or do I need 2f+epsilon?

[@voytechj]

In theory sampling at 2f is enough, in practice before ADC we need analog low pass anti-aliasing filter to get rid of frequencies >f. If you don't do that, noises from bats, etc. will "alias" to lower frequencies that can be audible by humans, which is bad. Analog filters are not perfect, 20kHz low pass filter still passes higher frequencies but with lower amplitude. So, we have to sample much higher to combat aliasing from imperfection of analog filters.

[@rsa5991]

Sampling at exactly 2f is sometimes enough, but in most cases isn't. It depends on the phase difference between the samples and the frequency at f. If the samples just happen to fall on peaks of "f" - the signal will be recovered exactly. However, if the samples fall in any other place - you get the frequency at "f" with a reduced amplitude. And if they fall exactly on zeros - the frequency at "f" will be lost. Of course, that's assuming we have a perfect low-pass filter to recover the signal.

[@strangelyrepulsive77]

how do you prevent sinusoidal dipleneration?

[@Gebm1223]

Hey Zach can you please make a video on Engineering Physics degree

[@hasanhuseyinuluay7057]

Just in time

[@michaelpowers6632]

I love your videos, but this is the very first time I understood almost 0% of this because I’ve never been exposed to this kind of content

[@fotgjengeren]

When my knowledge of music makes me familiar with much of the terminology in this video

[@Derps0]

Please make a video on convolution math I'm 2 months into signal processing and I still don't understand why I'm doing it.

[@Smallpriest]

Shannon the GOAT

[@TawsifTurjoeee]

How can you make these Videos? 😊

[@grln930]

DSP is goated. I'm and undergrad and really interested in the subject and I'm wondering where I could end up working in DSP in the industry. Do you have any tips where a career in DSP could lead?

[@delhimisedelcoda8716]

I don’t understand this, but I certainly hope too soon.

[@owlofwisdom]

I'm always confused when I come to this channel and get rational content.

[@IDoBeCalvingTho]

Oh my god I just found the math channel.

[@fhchowdhury1358]

Hi, How can I contact with you?

[@bedro_0]

I am willing, but not able to figure out the original signal.

[@daw6071]

best sampling rate for 32bit float

[@agod5608]

I want to follow.

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Daugherty Street

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I love you

[@StephaniePillar-u1z]

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[@Mark-dc1su]

Shannon-Nyquist can actually be beaten with compressed sensing!

[@WatYale-f1e]

Oswald Radial

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Kelly Light

[@ar3g0n810]

Next step is to sample non uniformly

[@JonesNelly]

2878 Streich River

[@schlast8311]

you really did not explain why that box has the size it does. This theorem cannot be really understand without the math.

[@BartBerg-h6m]

Josianne Summit

[@philipmrch8326]

And this is why high resolution audio is a scam

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😲😮

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[@unnamed7225]

the top comment is not sponsored by brilliant

[@ivanrodionov9724]

Great video, however I feel you missed an important point, the shannon theorem is a sufficient but not nessesary condition for reconstruction is only true for sinusoidal interpolation. In different bases things get very different, this is what compressed sensing works with.

[@MinMax-kc8uj]

It is nice to spend all my free time learning this stuff, but I'm forgetting it faster than I'm learning it. I'm looking at my math worksheets from 10 years ago and I have to figure it all out again. I think I'll leave this to those autistic people that have a freaky ability to absorb it all. I'll never be as good as they are. I'm going back to playing video games.