Shannon Nyquist Sampling Theorem

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This video discusses the famous Shannon-Nyquist sampling theorem, which discusses limits on signal reconstruction given how fast it is sampled and the frequency content of the signal.

For original papers:

This video was produced at the University of Washington

[Eigensteve]

A viewer made the excellent point that we technically need to sample at "strictly greater than" 2*omega. For the example, if you sampled at exactly 2*omega at the wrong phase, you could easily get something that looks constant.

[hyperTorless]

it's crazy how clear everything becomes when the teacher knows how to make pretty drawings.

[its.bonart]

Why isn't this man getting millions of views?!

[Via.Dolorosa]

I am really impressed by how you teach, your students are lucky.
You make science really attractive. Thanks prof.

[freecheese]

I have been a graduate student and have seen many presentations by Docs, PhD's, experts but this was a superb explanation and best backdrop.

[Pewpewlazorz]

Fun fact: In Solid State Physics, the periodic spatial arrangement of atoms in a crystal basically "samples" the physical properties related to waves traveling in the solid. One then uses so called "reciprocal space" which is just a 3D fourier transform of the crystal for easy mathematical description. The Nyquist frequency in that 3D reciprocal space denotes the so called "Brillouin Zone", which plays an important role in Solid State Physics. For example, it dictates a condition on the occurence reflexes in diffraction experiments for determining crystal structures.

[Bombad]

Great anecdote about why MP3s files are sampled at 44kHz. However, the extra 4kHz are there not because we can hear frequencies in the 21-22 kHz range, but because of how filters behave in practice. The extra frequency padding provides a good transition band for anti-aliasing filters.

Also, love your videos btw. Been watching since taking AMATH 301 :)

[weir-doe]

You should conduct an entry level communication module or signal and systems, this is really a masterclass quality explanation

[DJmates]

Steve, I really never comment on videos, but you are the best. If this can serve as a bit of motivation. please keep doing these amazing videos. You nail them every time. Let me finish by simply saying: Thank you!

[rtpwjkr]

What he said and clarified at 10:56 made me understand what I could not understand from so many formal texts. Thanks a lot.

[rammsund]

You can get a flat signal if you measure at exactly twice the frequency. Imagine a pure sine wave at 1 Hz. You measure at 2 Hz and only find a flat signal. Then you managed to start measuring at the inflection points of the sine wave. Thats why I sample above twice the frequency.

Excited about the compressed sensing series!

[ashwiniganesh]

Hands down, one of the best presented videos. Tools used + narration = Game on point.

[skaalduggery]

WOW...I have spent 3 years at university and they have failed to explain control/signals anywhere close to this. Love the energy dude!

[PaulinKantue]

I've learned something new today. Human hearing is up to 22 kHz. I've always found Nyquist Samping Theorem very fascinating. Thanks as always Steve!

[celine-]

Thank you so much for your great explanations! You are making very complicated topics easy to understand - without losing information and oversimplifying it. Please never stop teaching :).

[chrisesprey]

The point at which frequencies fold is at omega over two e.g. Nyquist. In the PSD plot you show the folding to occur about the sample frequency of omega. For instance a frequency at 0.6*omega would fold down to 0.4*omega. Great video though with a great explanation. Subscribed - looking forward to watching more of your stuff!

[steaminglobster]

Thanks for the video with intuitive. After watch your video, I think this way: Think the system as a black box, sample it at the 1X of highest frequency means you get a amplitude with no phase information, but with 2X sampling rate, you get the phase information, this amplitude and phase information gives you everything about this signal. It is like some aliens want to check what season the earth it is now, they need to check twice per year(they need to make sure within a year, the season). My two cents. Thanks again, I benefit a lot from your video.

[juliangomez]

Thank you Steve for making the most of this COVID year.

[afonsorafael]

Your classes here are looking really good!

[DGSEM]

Your videos are really good. Keep up the good work. It's fun to watch your videos.