Aliasing and Nyquist - Introduction & Examples

Please contact Analog Arts (analogarts.com/) and share your inputs, suggestions, and ideas with us. In this video, we talk about the basics of aliasing and how it effects imaging and audio digital signal processing. We use SL937 USB oscilloscope to show examples of the effect of aliasing when (at bigger time intervals,) the oscilloscope sampling rate is lowered and the Nyquist criterion is no longer met.

[@rafatulhauque7782]

1:20 cracked me up! A real example through audio lmao! The content creator must have a good sense of humor!

[@RenKohana]

Very good video. It's a lot of info at first, but after re-watching, it really starts to sink in. Thank you!

[@academia7768]

Thank you for watching and your comment.

[@anomalyp8584]

the propellor warping is a consequence of rolling shutter effect. Not directly because of aliasing

[@pasijutaulietuviuesas9174]

Why do people keep saying the Nyquist theorem allows the sampling rate to be *atleast* twice the highest frequency? Exactly twice the highest frequency would represent that highest frequency as a 0 on the y axis. It needs to be *more* than twice the highest frequency for the signal to be represented perfectly.

[@academia7768]

Thank you for your comment. redwood.berkeley.edu/bruno/npb261/aliasing.pdf answers your question in details. Theoretically, this minimum sampling rate is in fact correct since having two unique sample points per cycle is sufficient to define the sampled sine wave. Of course, for the special case that you lock the phase of the sampling signal such that it always passes through the middle point of the wave, you are absolutely right. In practice, however, we need much higher sampling rates than what the Nyquist theorem demands.

[@ronillorousso6870]

Great observation. But note that the Nyquist Theorem provides the correct MINIMUM sampling rate for a system. It does not set the sufficient requirement though. In other words if your sampling rate is below that of Nyquist, you would not be able to define the signal correctly.

[@DavidLindes]

@@academia7768 I believe that paper is wrong -- and thus, so is your video. See en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem#Critical_frequency - which mentions the requirement of a "_strict_ inequality of the sampling theorem's condition" (emphasis in the original). Earlier in the document, it also says "The sample rate must *exceed* the Nyquist rate for the samples to suffice to represent x(t)" (emphasis added) See also: musicweb.ucsd.edu/~trsmyth/digitalAudio171/Nyquist_Sampling_Theorem.html -- which quotes the Nyquist theorem as saying "A bandlimited continuous-time signal can be sampled and perfectly reconstructed from its samples if the waveform is sampled *over* twice as fast as it's highest frequency component." (emphasis added) For what it's worth, you're not alone in getting this wrong. An otherwise great video about this in the practical realm of digital audio uses equality rather than inequality as well. :) kzbin.info/www/bejne/pojNlYp5mrWarKM (which, interestingly, was recommended to me as the "Up next" for this video -- which I didn't even notice until after I'd linked to it, because I watched it a while back and wanted to reference it because of the nice oscilloscope stuff it did... but then I noticed it got this wrong, too! Oops!) Anyway, change ≥ to >, and you're good. Meanwhile, for you or anyone else interested in a deeper dive, but preferring a video format over papers and such, here's another video that gets it right (as shown and discussed at 27:09 in that video): kzbin.info/www/bejne/lYuadqV-bLqHg9U

[@hatimkhan913]

short simple and to the point

[@academia7768]

Thank you for watching Hatim.

[@hatimkhan913]

Academia thank u for great effort

[@stephenrobertson4605]

Aliasing doesn't cause digital images to look blurry. It causes them to look jagged. In the example with the blurry text, that is actually where anti-aliasing has been applied. The blurring is intentional to avoid the jaggedness, and although it looks blurry when zoomed in, it looks better than aliasing when zoomed out.

[@user-xz3kb4fc9s]

Awesome visual aids, I wish the textbook I'm reading used these

[@shruthi2423]

#sampling theorem is divided into two three types they are oversampling, Nyquist and undersampling. #nyquist sampling means perfect sampling ie fs=2fm. #undersampling means sample rate is below the perfect sample rate ie fs

[@guliyevshahriyar]

exceptional work!

[@AlienRelics]

I disagree in what may seem a subtle way. If you capture a signal with a sample rate exactly twice the signal frequency, it aliases to anything from the full amplitude to zero output, depending entirely on where in the phase of the signal the captured samples are taken. But this also means that if your capture rate is, say, 10Hz above that of the signal frequency, you will have a pulsing as the location of the captured samples changes on the waveform, creating a beat frequency of 10Hz in the sampled waveform. I welcome corrections.

[@academia7768]

Steve, thanks for your comment. You are exactly correct. The Nyquist theorem, stated at 19 seconds, clearly states the required sampling rate for a signal. Then at 30 seconds, an example demonstrate that. At 15 seconds another example shows a situation similar to what you are describing. It appears that, the video is in full agreement with you.

[@DavidLindes]

@@academia7768: Yes, Steve is correct. I disagree, however, that that's what this video says. At 0:19, you show "𝐅sampling ≥ 𝟸𝐅signal". This should be "𝐅sampling > 𝟸𝐅signal" (≥ becomes >). And the audio says "at least", which should be "greater than". More detail in a different comment subthread about this same point.

[@OMGtheykilledKenny42]

And this is why the CD Red Book spec of 16 bit 44100Hz (Nyquist frequency of 22050Hz) is standardized, and still used today :). But it really comes down to how the audio signal is mixed and mastered. Most adults can't even hear the full 20kHz.

[@tymothylim6550]

Good video! Helps me understand the criterion well :)

[@jirioto6089]

Let's use DA-AD conversion for re-sampling to keep steepness origin. Comparator operational amplifier can do it. Math-algorithmical ones(interpolation,LPF) creates global nonsenses even in audio. There is a many records, especially in movies, that combine 44100Hz music with 48k-192k sounds and dialogs. And its bad, when they using virtually re-computed signals in mixture. Class-A signal processing is the only way.

[@akashjain35]

1:19 someone help him... he is drowning

[@jacobjacob6154]

That was very helpful. Thank you.

[@afshin3k3]

It is wrong F_sampling should be > 2F_signal. In the video they have written >=.

[@SunRaven]

Great explanation, thank you. ^_^

[@tachometer-flac]

What TTS voice is that - I like it. Reminds me of the joke by Stephan Hawking, "yo mama so fat her escape velocity exceeds..."

[@gurratell7326]

Many of the examples in this clip is not aliasing, so better to look for other videos if you want learn what it actually is.

[@zbra_maarten]

Thank you stephen hawking

[@jackcimino8822]

What is the text to speech called?

[@academia7768]

There are many text to voice tools, we tried. Unfortunately, most lack quality. We perform a post processing to enhance the voice.

[@jackcimino8822]

Academia I'm asking if you remember which voice you used in the video.

[@phasorsystems6873]

Circuits giving you a nigtmares? investigate androidcircuitsolver on google

[@MPYboys]

thumbs up plz Hello