The intuition behind the Nyquist-Shannon Sampling Theorem

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[@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 ✅

[@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!

[@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.

[@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

[@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

[@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!

[@146fallon9]

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

[@theDreadedBlur]

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

[@martinoffi9249]

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

[@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. 🙏

[@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

[@ultramohitb]

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

[@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.

[@KevlarSammy]

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

[@fast_gtr]

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

[@lMINERl]

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

[@chri-k]

it works!

[@nicholas_obert]

Wow

[@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

[@SamuelBelton]

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

[@user-kw5qv6zl5e]

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

[@HesterClapp]

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

[@retroforager]

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

[@gregorymccoy6797]

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

[@dylanparker130]

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

[@aaqilkhan]

Nicely explained. As always!

[@ProfeARios]

Excellent video. Greetings from Panama 🇵🇦

[@das224]

The bit on aliasing is a GREAT visualization =)

[@brianhershey563]

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

[@user-kf2qs2hg1f]

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

[@md.adnannabib2066]

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

[@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!

[@agastyasanyal4026]

Omg Zach PLEASE make a convolution video ❤

[@michaelrogers1066]

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

[@Saens406]

my favorite theorem of all time

[@adityamaniraja8464]

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

[@ColissaPollard]

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

[@BiplobHossainSorker]

thanks ❤

[@zajlord2930]

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

[@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

[@yusufserandogmus4118]

Love it

[@galdali10]

You should make more videos like this

[@DoktorSchaedel]

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

[@oskarkrogsgard3014]

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

[@lucykitsune4619]

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

[@ashwininir9535]

Goat

[@richardtrager7125]

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

[@thanoskarvouniaris6827]

Signals & Systems my favourite course in EE

[@1972hattrick]

Didn’t like DSP?

[@hsavietto]

This math is so dense my head Hertz.

[@GabrielBorges-fw7iu]

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

[@hasanhuseyinuluay7057]

Just in time

[@STEMHub18]

Finally after 69 years we get to see another nerdy video.

[@EvenMoreCheese]

Goatt

[@strangelyrepulsive77]

how do you prevent sinusoidal dipleneration?

[@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.

[@khaledelsayed3507]

Great

[@ozzymandius666]

I want to know why an 8-bit bit sampling depth won't show me real distortion levels on a 16 or 24 bit signal, even if the sampling rate is much higher than the frequency of the signal.

[@delhimisedelcoda8716]

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

[@Smallpriest]

Shannon the GOAT

[@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?

[@user-om4by2ig8g]

How can you make these Videos? 😊

[@fotgjengeren]

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

[@agod5608]

I want to follow.

[@owlofwisdom]

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

[@fhchowdhury1358]

Hi, How can I contact with you?

[@SpunckyJew6969]

I love you

[@Mark-dc1su]

Shannon-Nyquist can actually be beaten with compressed sensing!

[@bedro_0]

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

[@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.

[@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

[@juliasteam2077]

Is this aliasing the same thing as in computer graphics (anti aliasing)?

[@bedro_0]

in both cases, aliasing refers to imprecision due to insufficient sampling. A pixel is also one sample of an image in 2D space, and aliasing happens due to a lack of pixels. Maybe someone with a little more knowledge can correct or add on this idk

[@ar3g0n810]

Next step is to sample non uniformly

[@philipmrch8326]

And this is why high resolution audio is a scam

[@Negreb25]

😲😮

[@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.

[@realcygnus]

nifty

[@unnamed7225]

the top comment is not sponsored by brilliant

[@brian420pm]

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