2. Sampling Theorem - Digital Audio Fundamentals

Рет қаралды 69,411

Күн бұрын

In this video, we take the first step at the process of converting a continuous signal into a discrete signal for processing within the digital domain, and take a stab at the Nyquist Shannon Sampling Theorem which dictates how often a continuous signal needs to be sampled to accurately recreate it back. There is a lot of misconceptions regarding sample rate and its implications, and this video should hopefully help in clear them up by looking at sampling rates more objectively, or atleast give you a starting point for more exploration.
Find the full playlist here: • Digital Audio Fundamen...
Content:
0:00 Continuous vs discrete signals
2:35 Nyquist Shannon sampling theorem
5:53 Bandlimiting using low pass filter
6:40 Sampling examples in Audacity
12:30 Re-conversion of digital signals to analog signals
16:43 Aliasing artifacts
19:20 Practical sampling rate and outro
Audacity (Free audio editing software) - www.audacityteam.org/download/
References:
Principles of Digital Audio by Ken C. Pohlmann
Analog / digital demonstration with hardware analog equipment - xiph.org/video/vid2.shtml
This video series explains the fundamentals of digital audio, how audio signals are expressed in the digital domain, how they're converted and transformed and the limitations of working with digital signals.
If you've got any questions, suggestions or recommendations, type them out here, or send me a message on any of my social channels mentioned below.
A lot of time was spent on creating this series, and I plan to do more. So please consider subscribing if you wish to be notified about more releases in the future. And if you feel generous: / akashmurthy
Check out the audio track in the intro and outro here: / tinderbox
Check out my music here: farfetchd-official.bandcamp.com/
Give me a shout here:
Facebook - / akash.murthy.319
Instagram - / thrifleganger

Пікірлер: 252

@user-wc1sr7ci6h 3 ай бұрын

this might be the best video explaining those digital signal processing concepts

@guidoschilliger Жыл бұрын

I only discovered these videos yesterday and I am simply blown away. Thanks a lot for putting in all this enormous effort to make them, Akash. These are extremely well done and the subjects are excellently explained. Fantastic work! 🙏

@akashmurthy Жыл бұрын

Thank you so much! I'm glad you found the channel.

@artpinsof5836 5 ай бұрын

I also have had my mind blown after discovering these videos "yesterday" (1 year after your comment 😅)

@ishaanpareek5751 4 сағат бұрын

best video ever for audio processing

@oscartrillionaire247 3 жыл бұрын

Man, you are more knowledgeable than the best professors in the world. Your way of explanation is phenomenal. Keep patience mate, you will reach more than a million subs in the next couple of years. Keep making these videos, you are serving humanity in a very very positive way. Thanks a lot

@akashmurthy 3 жыл бұрын

Thanks a lot for the compliments man! Although, I don't pretend to know it all. All of these videos were researched thoroughly, and I learnt quite a lot while doing that. And yet, there are a few mistakes here and there, that I discovered later. It's a learning process for me, as it is for you! But I really appreciate the positive feedback, and yea, I'll continue to do more.

@mouhamadalmounayar2199 4 ай бұрын

I cannot express how much I love this video

@akashmurthy 4 ай бұрын

Aww, thanks very much!

@mikkokylmanen9296 3 жыл бұрын

Wow! I am stunned by the quality of your videos, they are just perfect. I'm new to the topic and this is hands down the best video I've yet seen on it.

@akashmurthy 3 жыл бұрын

Thanks a lot of checking it out!

@VU3FKA 2 ай бұрын

This shows the depth of your understanding and your willingness to share the knowledge with others. Excellent work 👏👏

@akashmurthy 2 ай бұрын

Thank you so much for your feedback!

@lil_works 3 жыл бұрын

You are doing an amazing job man !! This playlist is so helpful 👀👀

@akashmurthy 3 жыл бұрын

Thanks very much!

@MARISBENMusic 3 жыл бұрын

You are saving my university year!

@akashmurthy 3 жыл бұрын

Haha..good luck with college!

@lil_works 3 жыл бұрын

Saving mine too 🤣

@kswindia 3 жыл бұрын

These videos are pure Gold Akash! Really well produced and well chalked out. Massive props 🙏🏼

@akashmurthy 3 жыл бұрын

Thanks a lot! :)

@jasonlabatti7475 2 жыл бұрын

I second this. Excellent videos! Using these to help my students better visualize the process in my computer science class now. Thanks, Akash! Very well done.

@akashmurthy 2 жыл бұрын

Thank you Jason! I'm glad you're able to use these in an academic setting!

@leploeo7145 2 жыл бұрын

probably the most underrated series of videos on youtube

@RenatoAkira18 3 ай бұрын

This series of videos are simoly amazing! Thank you so much for explaining audio processing that way :)

@akashmurthy 3 ай бұрын

Thank you! I'm glad you found these useful!

@eglenausedaite9794 3 жыл бұрын

Awesome, Akash! You speak so clearly and interestingly.

@manjunathanj9316 2 жыл бұрын

This video is something else... The quality of explanation and animation are so good. Now I can do seminar about this topic without hesitation.

@akashk961 2 жыл бұрын

Congratulations, I can sense your dedication. All the best ahead with your new works! 😎👍🏻

@SenthilKumar-ib1wu 3 жыл бұрын

The process of recording sound stored in the form of thousands of indivdual measurement each at a discrete unit of time called.. very thanks for a super video....

@rafilushan1988 3 жыл бұрын

That's the best representation of sampling!

@Peaceful-er4vf 2 ай бұрын

Amazing. Absolutely amazing animation and explanation on this concept. Thank you for the fantastic work!

@akashmurthy 2 ай бұрын

Thank you so much for the support! :)

@thedarklordofcats339 3 жыл бұрын

A god amongst men. Thank you for representing concepts in easy to digest youtube videos! Reading university books is so draining by comparison lol

@akashmurthy 3 жыл бұрын

T'is but a man, but a man with time. Thanks mate, glad you found it useful!

@satbun477 2 жыл бұрын

the qualities of this video is extraordinary !!, you deserve more subscriber and views thank you so much

@sumantnemmani4877 4 жыл бұрын

Amazing video! Love the explanations, the visuals and production overall! Subbed.

@akashmurthy 4 жыл бұрын

Thanks for checking it out!

@workethicrecords5901 3 жыл бұрын

This Channel is amazing, and is filling in a lot of holes made by my DSP professor. Great stuff

@akashmurthy 3 жыл бұрын

That's high praise! Thanks very much :)

@MrSouzy 3 жыл бұрын

many thanks for the video. When you said that it was a mathematically unique solution combined with the graphic it clicked in my head because I realized even before you said it that only one wave form at a certain frequency form could pass through all of the points at that same time. Really interesting !

@akashmurthy 3 жыл бұрын

Great! I'm glad the graphics were useful.

@FirmanAsa 2 жыл бұрын

The graphs and animations complement your explanation really well!

@akashmurthy 2 жыл бұрын

Thanks very much!

@MM-ry4ki 2 жыл бұрын

Since my knowing of this theorem, I have always tried to understand this.This video really makes me to understand.Thanks.

@akashmurthy 2 жыл бұрын

Glad it helped you out!

@FreedomForKashmir Жыл бұрын

This is super high quality precious content ... made with effort and commitment. No only his theoretical concepts are clear but also way of transforming them and explaining them is very good Much appreciated

@akashmurthy Жыл бұрын

Thanks very much mate! :)

@user-gw5lc2ks2v Жыл бұрын

the quality of your vidoes are so good u def deserve more subs

@akashmurthy Жыл бұрын

Thanks mate!

@srinivasprasanth8703 3 жыл бұрын

Your way of explanation is awesome🔥.Thanks for making this video

@akashmurthy 3 жыл бұрын

You're welcome! Thanks for checking it out..

@kreczu77 9 ай бұрын

This is where the maths and physics are NOT boring. Your explanation is genius Akash. Thank you

@akashmurthy 9 ай бұрын

Thanks so much mate!

@happyBellaXD Жыл бұрын

Thank you so much for the series! You made it so clear and easy to understand, just amazing

@akashmurthy Жыл бұрын

You're welcome! Glad you found the series useful!

@timoluetk 2 жыл бұрын

This video series is seriously amazing!

@akashmurthy 2 жыл бұрын

Thanks very much mate!

@RitwikKaikini 4 жыл бұрын

Very cool stuff man! loving your tutorials.. Am very glad you have embarked upon this journey.... There's always something new to learn! good stuff.. keep it up! :) cheers

@akashmurthy 4 жыл бұрын

Thanks man! The plan is to continue deep diving into audio concepts and getting as low level as possible while still being engaging and accessible enough. Thanks for the support, and for checking it out!

@DAXBRWNMUSIC 9 ай бұрын

these videos are very well explained and put together. thank you!

@akashmurthy 9 ай бұрын

Thanks very much!

@tim3.1415 11 ай бұрын

Such a high quality video! Thank you for this, such an enrichment for this platform.

@akashmurthy 11 ай бұрын

Thanks mate! :)

@fahadzhossain Жыл бұрын

Bro you are just awesome. Your animation and the fluency of describing is mind blowing. Love to watch your videos. Keep it up brother.

@akashmurthy Жыл бұрын

Thanks very much mate!

@UDiAudio 3 жыл бұрын

Excellent video and presentation.. I can already imagine this channel with 10K subs in few months from now. Good luck.

@akashmurthy 3 жыл бұрын

Cheers! Thanks for taking the time out to write that!

@agustin2881 Жыл бұрын

its just so nice to find good content in non common topics. thks it helped me.

@akashmurthy Жыл бұрын

Glad it helped mate!

@Apeskinny 3 жыл бұрын

Love this! And the nod to Monty 😊👌

@carlosa.chacon985 3 жыл бұрын

I was going to write the exact same thing lol

@DankBurrito420 5 ай бұрын

Hey Akash! I recently found your videos and they are a blessing. I'm an Audio Engineer and Comm. Studies (with emphasis in Film & Media) major, that has been working in professional A/V for the last 5 years now. This series is helping me study for CTS, and just overall knowledge refresher. Thank you!

@akashmurthy 5 ай бұрын

That's awesome to hear, thanks for sharing!

@wilmercohen3764 2 жыл бұрын

I always sample at speeds well above that established by the theorem, since that way I can dispense with the design of very high-order filters that resemble ideal filters as much as possible, and use low-order filters... although of course this implies that electronic devices must also be able to handle such high frequencies. A very educational video

@huyhuynhquang3004 8 ай бұрын

Love your effort and time you put in one video, it just phenomenal, i learn a lot from it. Thank you so much

@akashmurthy 8 ай бұрын

Thanks so much!

@Apeskinny 3 жыл бұрын

Man , that visualisation of aliasing is awesome!!

@akashmurthy 3 жыл бұрын

Cheers man! There another video in the series, number 4, that talks about aliasing with a bunch more visualizations. Thought that might interest you!

@amidall Жыл бұрын

Hey, you make learning so easy for me by making these videos. They are well produced, the tempo is perfect, all the necessary information is included and your lecturing style makes it seem like you go through the thinking process alongside us which really makes understanding all this completely effortless. Great great work!

@akashmurthy Жыл бұрын

Thank you very much! I'm glad to hear you like the style of the videos. It was an intentional choice to go through all the common questions that I had when learning these concepts and answering them.

@amidall Жыл бұрын

@@akashmurthy could you do a series on acoustics?

@akashmurthy Жыл бұрын

@@amidall any particular topics in acoustics?

@Yogachara Жыл бұрын

Excellent presentation. Your videos are so freaking good

@akashmurthy Жыл бұрын

Thanks a lot mate! :)

@exxzxxe 2 жыл бұрын

Really well done! Concise, clear and correct. Thanks.

@akashmurthy 2 жыл бұрын

Thanks mate!

@ptsdon 2 жыл бұрын

Akash isn't a good explainer. He is a GREAT explainer. I am very impressed!!😊

@akashmurthy 2 жыл бұрын

Thank you kind sir!

@Peaceful-er4vf 2 ай бұрын

Amazing work!

@Shanmuga 10 ай бұрын

Incredible stuff!

@AyonAbeywickrama 2 жыл бұрын

Thank you for the content dude love em! This is truly valuable!

@musicgpaul 2 жыл бұрын

Thank you so much for these lectures!!

@CannedMan 2 жыл бұрын

Beating is what is used for tuning pipe organs. The pipes called principals have the least amount of tuning degradation over time, so to tune the other voices, you pull the principal plus the desired voice, then listen to the beating; tuning the desired voice is then done by miniscule adjustments of that voice until the beating stops.

@danieliniguezv 3 жыл бұрын

my God! your work is simply amazing. thank you so much!!!

@akashmurthy 3 жыл бұрын

Thanks so much man! :)

@baleeghal-baitar 5 ай бұрын

Thank you from the bottom of my heart,now I understand the sampling theory. I’ve been attending the lectures and the doctor keeps talking about it and never understand what he says 😅

@akashmurthy 5 ай бұрын

Haha, that's awesome! It's quite simple, once you get a hang of it..

@SAJAN_ECE 2 жыл бұрын

Amazing video! Thanks for the efforts.

@danielolmos5484 Жыл бұрын

Great quality video, super helpful! Thank you

@akashmurthy Жыл бұрын

Cheers mate!

@varunvenu88 4 жыл бұрын

Amazing experience!! the engineering nyquist theorem is enlightening!

@akashmurthy 4 жыл бұрын

Hey I'm glad you found it useful!

@CULTUM_d 3 жыл бұрын

RESPECT for the top quality videos 🧠 way better than most uni lectures

@akashmurthy 3 жыл бұрын

Cheers mate!

@Isabellaa-ms5dk 10 ай бұрын

your videos are amazing.

@ramseybolton1509 2 жыл бұрын

6:22 I realized few seconds later its you voice! Graphics : 100/100

@akashmurthy 2 жыл бұрын

Yea! It was quite easy to do, but thanks for noticing!

@stefansoaremusic2699 8 ай бұрын

Awesome video mate thanks for the great work❤

@akashmurthy 7 ай бұрын

Cheers mate!

@aashman Жыл бұрын

Congratulations Akash...The kind of quality it contains surprised me....Initially, I thought it was done by some American guy...

@davidasher22 3 жыл бұрын

Akash, you are in my brain right now!

@akashmurthy 3 жыл бұрын

Sorry to intrude 😅

@Time-cc2qb Жыл бұрын

These are amazing man

@akashmurthy Жыл бұрын

Thanks a lot man!

@BorisNienke 3 жыл бұрын

first i was about to draw some panels to illustrate the Sample-Rates and what it means to higher frequencies. Then i thought, i should first look if someone already did it so that i could simply share a link. THEN i found THIS one and learned more details on something i though i already knew :D - Thank you!

@akashmurthy 3 жыл бұрын

Glad you found it helpful, thanks!

@YandereEnthusiast Жыл бұрын

Thanks a lot man, this video was really helpful!

@akashmurthy Жыл бұрын

Thanks for letting me know!

@Dnlrmrez Жыл бұрын

Bro your videos are so well done thank you

@akashmurthy Жыл бұрын

Thanks bro! :)

@aftofono Жыл бұрын

such a shame I didn't discover this earlier, very well explained, very well produced, thank you!!!

@akashmurthy Жыл бұрын

I'm glad you discovered it now!

@mekishethio8738 2 жыл бұрын

I love this video a lot. Thank you. God bless you

@akashmurthy 2 жыл бұрын

You're welcome! :)

@paolopasqua14 Жыл бұрын

awesome! Thank you for your job.

@aathifahamed547 2 жыл бұрын

actually this is so awesome... god bless you.........

@ishykashy 2 жыл бұрын

You are an amazing teacher. Thank you!

@akashmurthy 2 жыл бұрын

Thanks a lot mate!

@leploeo7145 2 жыл бұрын

thanks for this amazing content

@gustavoalvarez6637 2 жыл бұрын

Excellent video!

@akashmurthy 2 жыл бұрын

Thank you! :)

@NISSIHYPERCORP 2 жыл бұрын

I love the way you explain it 💖 The way you work on each topic which seems complex You are incredible The graphics and voice are really making it a pleasant learning of joy Please dont stop 👍 I love the way you put real life into dumb equations .

@akashmurthy 2 жыл бұрын

Thanks a mil for all the kindness!

@irethoronar34 2 жыл бұрын

Crystal clear.

@Rene_Christensen 3 жыл бұрын

Small mistake at @4.20 as it is 1/s not 1/s^-1. But this is one of the best videos on this topic.

@akashmurthy 3 жыл бұрын

Great spot! Thanks..I cringe at this mistake whenever I watch it back.

@Rene_Christensen 3 жыл бұрын

@@akashmurthy Don’t sweat it. It is impossible to make a video without small mistakes and it does not detract from your great information. Watching your dither videos now.

@salvageddoor 2 жыл бұрын

Amazing video, so informative

@akashmurthy 2 жыл бұрын

Thanks mate!

@rainyafternoons7003 2 жыл бұрын

thanks so much! all of this very much applies to sdrs and radio so it is really helpful for me!

@akashmurthy 2 жыл бұрын

Thanks mate! I'm glad it's helpful to you in your domain! First time I heard of SDR today!

@rakshithvshetty1551 3 жыл бұрын

hey man loved this video

@SLigHtOfView Жыл бұрын

Great vid made a very complicated subject a bit easier to grasp, still got a lot to learn lol

@akashmurthy Жыл бұрын

Cheers mate! Always a lot to learn I'm afraid..

@suyashramteke3588 7 ай бұрын

Simply Genius!!

@AnalogDude_ 28 күн бұрын

very good video.

@tombrooks5118 Жыл бұрын

Wow, I came to your site to learn PCM which you will cover in part 9 or 10 and here as a bonus you have covered the free DAW software Audacity which as a beginner hobbyist, I actually want to learn to use with my music keyboard and computer. You showed us amazing things Audacity can do much better than sites dedicated to Audacity have shown me. Its like an Oscope and a spectrum analyzer. I want to watch all of your videos.

@akashmurthy Жыл бұрын

Audacity is a powerful software for sure! All the best with your learning.

@senmonkashonen5875 Жыл бұрын

thanks a lot, keep up the good work.

@akashmurthy Жыл бұрын

Thanks for checking it out..

@lordpatil7716 3 жыл бұрын

You have a new Sub!

@carlosa.chacon985 3 жыл бұрын

Montyyy! Awesome Channel man!!

@akashmurthy 3 жыл бұрын

Cheers man! Yea, xiph.org is great!

@gherbent Жыл бұрын

All good, apart from two things. 1. Is really difficult to band limit a signal with such a steep filter. I am talking abut recording real audio signal , not a generated one, and encoding to CD digital format. 2. The theorem works, and is true to identify only sinusoidal signal long enough in time, and constant in frequency and amplitude. In case we approaching the upper limit of the band , and the pulse is short we may not have enough iterations to correctly identify a signal. Example is; the occurrence of one single wave in 19KHz band recorded with a CD standard 44.1KS/s. The real audio consists at most of fading impulses, rather than long in time and continuous in amplitude sinewaves, that is why I consider the CD format to be lossy and a higher sample rate well be beneficial, 48 or 96KS/s. The reconstruction of impulses by DACs is often an approximation.

@rollyverma8958 Жыл бұрын

You are gems

@amarmohanta2516 2 жыл бұрын

Thanks sir🥳

@blackseastorm61 2 жыл бұрын

came here from signals-systems & DSP courses, because of stucking in sampling and continuous-discrete conversion. I have to say that, this video is quite good at explaining the subject intuitively and visually. It can be said that you are showing both whole and the pieces of the topic, this is a good approach to explain it. Sampling-Discretization-Periodization-Modulation, these topics needs to be explained well. I have still problems on understanding the CT to DT conversion, how this conversion occurs mathematically ? I mean, how to transform continuous time x(t) to sequence x[n] , mathematically? what is the operator that converts ""impulse(t) >> to impulse[n] with amplitude of 1"" or ""x(t) . p(t) impulse train >> to x[n] as a sequence"" x(t) . p(t) could be represented as = summation the series of x(nT) . impulse ( t - nT ) But this is still not equal to a sequence of x[n] , because it contains scaled impulses with amplitude of infinity, right? Therefore I am trying to understand what actually this conversion and this impulse are. What is the title of topic/video that covers this point? Thank you for helping.

@jwfarknar 3 жыл бұрын

Love the well constructed animation content along with excellent spoken explanations. I can almost just listen or just watch and still get 90% of the meaning. In addition to your good ear, you also have a good visual design eye :) What software tools are in your video content creation editing toolkit?

@akashmurthy 3 жыл бұрын

Thanks mate! I'm glad you find the content understandable! Yea, I really wanted to bring the visual element out as much as possible, not just functionally, but aesthetically as well. I use Adobe After Effects for the motion graphics and video editing, that's the only tool I use. And I use Reaper for audio.

@jwfarknar 3 жыл бұрын

@@akashmurthy Fast reply and right to the point! Thanks :)

@abhijithas9976 2 жыл бұрын

Thankyou sir

@user-go6kw3ye3u Жыл бұрын

nice video

@piyushparashar8990 2 жыл бұрын

Very nice video! Thank you very much. Questions to you - why do we need band limiting when the original signal in Audacity is to be created for 3.999KHz ? Where will the high frequencies come from which are to be band limited? And if there are higher frequencies, wouldn't we need to sample w.r.t that value (Fmax will change)? Thanks again.

@fawzial-tawil1643 2 жыл бұрын

you know, your agreat thx for every thing

@suttikorntocharoenniwatsai9447 3 жыл бұрын

A great video and explanation. But I'm confusing some points that you explained. @17:07 about the extra high-frequency content. Why it has an extra high-frequency content even if the generator produced the pure single signal at 3.9kHz?