Sampling Rate, Nyquist Frequency, and Aliasing

[thehotsteal]

short and sweet an very helpful . thnx

[MrGeneralRelativity]

Now I see why it's 44.1 and not 44! hhh THNX!

[jonahansen]

Wow - the arrogance and condescension in these comments almost approaches the idiocy of comments in standard, non-technical youtube videos. Dr Dave said nothing wrong, really; there is a lot more to sampling, as many have touched upon, regarding reconstruction of the original waveform, etc. But he is not "flat-out wrong", he's quite correct as far as he goes, and it is a good demonstration of a basic principle of sampling. Dunning-Kruger effect anyone?

[NotATube]

@jonahansen; I'd prefer "arrogance and condescension" than the spread of misinformation.

I'm no expert, but AFAIK Nyquist-Shannon does *not* state that the samples (or rather, the waveform recreated from them in the "join the dots" manner seen here) represents the final reconstructed output as implied.

If that's not what the video is saying, then it needs to be clearer, because it's either very misleading or wrong.

[NotATube]

@jonahansen; (continued)

My understanding is that reconstruction of the signal is achieved by passing a train of impulse value spikes (from the sample points) through an f Hz filter (assuming the original sampling was done at 2f Hz).

If anyone knows better, please correct the above.

BTW, does anyone know if the unfiltered "join the sample values" waveform the video shows will give the same output as the equivalent train of sample-point impulses *after* both have been f Hz low-pass filtered?

[ansosify]

good job, some equations might help get the idea accrooss as well :)

ty

[afreshcupofjoe]

DrDaveBilliards does not understand sampling theory. The amount bad information presented in the comments section of this video is astounding. Please get your information elsewhere.

(Sorry Dave. Nothing personal. I just don't like to see bad science being spread on the internet.)

[DrDaveBilliards]

@afreshcupofjoe

Why don't you post a video showing how a reconstruction filter reproduces a signal (e.g., a simple sine wave) from various sample sets at different starting points on the wave, with a sampling rate just above Nyquist. That would be interesting and useful, and I would be happy to accept it as a video reply.

Thanks,

Dave

[DrDaveBilliards]

@DrDaveBilliards - cont.

Obviously, if a "reconstruction filter" is not being used, you need to sample faster to get a better representation of the signal (e.g., if you just plot the raw sampled data). Most of my comments were dealing with simple plots of raw sampled data.  I would certainly like to learn more about reconstruction filters

Thanks again,

Dave.

[afreshcupofjoe]

@DJPeteJames

44kHz is plenty of bandwidth to accurately represent audio recordings. This is exactly what Nyquist's Theorem shows us. 48khz can be slightly better, but that is only because it's better to have more than 4 khz of gaurd band. It has nothing to do with the fact that 44kHz isn't adequate to capture the original signal. Going up to 96kHz is absolutely pointless if you just want to preserve the original signal. Increase bit depth if you want more fidelity.

[MrTre144]

Hello. I am curious to know why the representation is degraded when going slightly over the Nyquist rate. It was my understanding that anything above his rate would offer a better reproduction of the original signal.

[DrDaveBilliards]

@MrTre144

You must sample at greater than the Nyquist frequency to prevent frequency aliasing. To get a high-fidelity representation, you must sample much higher than the Nyquist rate. At a rate just above the Nyquist frequency, the fidelity is poor, but there is no frequency aliasing. There is aliasing at frequencies below Nyquist.

[afreshcupofjoe]

@DrDaveBilliards

This is not correct. At a rate just above Nyquist the fidelity will be just as good as sampling at 10x the nyquist frequency. It doesn't effect fidelty. The problem arises when you have a signal with additional (inaudible) frequency content higher than the nyquist frequency, as occurs with audio signals recorded from an analog source. You must first low pass filter the signal in order to remove the high frequency content, but no filters are perfect...

[BDGregory]

@afreshcupofjoe

I guess you only need a good filter if the extra components above the Nyquist frequency are in the audible range or might cause problems to the audio equipment it's driving.

[DrDaveBilliards]

@afreshcupofjoe

This depends on your definition of "fidelity." Using the typical audio definition, sampling at 44 kHz (which is more than twice the highest frequency perceptible by typical humans with good hearing), results in high fidelity (i.e., no frequency aliasing). However, if trying to capture and plot a waveform precisely (with good amplitude resolution), you must sample much fast faster.

[afreshcupofjoe]

@DrDaveBilliards: This is just flat out wrong. There are many sources of inaccuracy in real-world conversion systems that can cause signal degradation, but (beyond Nyquist) they are not the sample rate. In fact, using a higher sample rates actually decreases accuracy, while offering little other benefit. Please cite sources if you are going to make such unfounded claims.

A technical discussion of the subject can be found here:

ɟpd˙ʎɹoǝɥʇ‾ƃuıןdɯɐs/sʇuǝɯnɔop/­ɯoɔ˙ƃuıɹǝǝuıƃuǝʎɹʌɐן˙ʍʍʍ//:dʇʇ­ɥ

[DrDaveBilliards]

@afreshcupofjoe

Thank you for the document link. BTW, case seems to be important ("Sampling_Theory" works, but "sampling_theory" does not).

I'll read through your document when I can find some time, and I will reply if I think it necessary or appropriate. The document looks like a good resource for people who want to explore the details more.

BTW, how did you create the upside down text that fools YouTube's URL blocker?

Thanks,

Dave

[afreshcupofjoe]

@DrDaveBilliards

continued... but no filters are perfect, so you must sample slightly higher than nyquist in order to create a guardband.

However none of this answers MrTre144s original question of why the signal is degraded. The answer is that the signal is not degraded at all. You are seeing a sampled representation of the signal, not what actually appears at the output. After being passed through an ADC, which contains a reconstruction filter, the original signal will not be degraded.

[DrDaveBilliards]

@afreshcupofjoe

Good point. As long as there is no frequency aliasing, the original waveform can be reconstructed fairly well (although, not perfectly). With faster sampling, the waveform will be better (i.e. have higher "fidelity").

[afreshcupofjoe]

@DrDaveBilliards: No it will not be "better'. You do not understand the Nyquist sampling theorem. (See my other comment for further explanation)

Please, please, stop posting comments like this if you don't understand what you are talking about. Sampling theory is a fairly complex topic, and it really does an injustice to people who are trying to learn the theory when you spread false information. I commend you for trying to help people with this video, but please learn the proper theory.

[Roskow12]

If you're looking to learn about the theory of the nyquist rate, disregard this comment, it is incorrect.

[dvamateur]

It would be nice if we could hear what the aliased signal sounds like.

[DrDaveBilliards]

Agreed. If you go to my video demos website (see the link in the video description), several examples can be heard under "Vibration and Sound."

[DrDaveBilliards]

44kHz, not 44Hz!!!

[DrDaveBilliards]

I don't know much about synths; but you are right that if you don't sample at a high enough frequency, amplitude and frequency aliasing can occur, regardless of the original source (analog or not).

[Shredder249]

cheers man, this was really good.

[DrDaveBilliards]

Thanks.

[Ba3dadBoy]

Sweet thanks, its nice to see it in real life

[DrDaveBilliards]

You're welcome.

[okturus]

when you go above the nyquist freq. , you encounter amplitude modulation right? how much higher do you have to go? could you be more specific than just "well above the nyquist" to avoid that modulation? like, is it an integer multiple of the the signal being sampled?

[DrDaveBilliards]

I don't know of any magic number here. The answer depends on what type of amplitude fidelity you are looking for.

[afreshcupofjoe]

@okturus

Any time you have audio content above Nyquist you will get aliasing. Up to the sampling frequency, the higher you go above nyquist, the lower in frequency the aliasing will be. Nyquist is at 1/2 the sampling frequency.

I guess you could call aliasing "Amplitude modulation", since it's the same thing mathematically, but the term "Amplitude modulation" usually refers to a low frequency modulating a high one, so I would generally avoid it when talking about aliasing to avoid confusion.

[okturus]

@afreshcupofjoe thanks :)

[eerereps]

thanx!

[DrDaveBilliards]

You're welcome!

[BDGregory]

This just proves you don't understand the theory. You have to have a filter on the output if you want to avoid aliases above the Nyquist frequency distorting the output. Only then will inputs near the nyquist frequency pass though the system undistorted. Just how near you can go to the Nyquist frequency depends on how good your filter is.

[DrDaveBilliards]

Good point.

The point of the video is to show what happens if you don't do this.

[afreshcupofjoe]

@BDGregory

Finally somebody who actually understands the theory. I felt like I was at a retard convention reading the comments on this video.

[stylefighterdks]

very interessting!

[ssdpjp]

thankyou for post

[DrDaveBilliards]

You're welcome.

Dr. Dave