2. Sampling Theorem - Digital Audio Fundamentals

[@guidoschilliger]

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]

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

[@artpinsof5836]

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

[@prajaktamajalekar5688]

Me too I'm blown away awesome ❤

[@AxelSyranoPedemeKuenzob]

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

[@oscartrillionaire247]

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]

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.

[@MARISBENMusic]

You are saving my university year!

[@akashmurthy]

Haha..good luck with college!

[@lil_works]

Saving mine too 🤣

[@mikkokylmanen9296]

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]

Thanks a lot of checking it out!

[@jpp2310]

The greatest vidéo about Shannon-Nyquist Kotelnikov theorem

[@leploeo7145]

probably the most underrated series of videos on youtube

[@VU3FKA]

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

[@akashmurthy]

Thank you so much for your feedback!

[@kswindia]

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

[@akashmurthy]

Thanks a lot! :)

[@jasonlabatti7475]

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]

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

[@thedarklordofcats339]

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]

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

[@lil_works]

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

[@akashmurthy]

Thanks very much!

[@mouhamadalmounayar2199]

I cannot express how much I love this video

[@akashmurthy]

Aww, thanks very much!

[@kreczu77]

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

[@akashmurthy]

Thanks so much mate!

[@MM-ry4ki]

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

[@akashmurthy]

Glad it helped you out!

[@jpeo98]

i will say it again, its so good it deserves more views. 10/10 video, its actually unusual to be so clarified just on the video alone. You have the awarness and intelligence to teach. Kudos to you my friend

[@akashmurthy]

@@jpeo98 thank you very much for the kind comments!

[@SenthilKumar-ib1wu]

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....

[@Peaceful-er4vf]

Amazing work!

[@DankBurrito420]

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]

That's awesome to hear, thanks for sharing!

[@SazzadHissain]

Hi Akash, sounds like you have put the nyquist shannons sampling theorem wrongly. Wouldn’t it be “greater than twice” instead of “at least twice”? 3:35

[@suttikorntocharoenniwatsai9447]

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?

[@manjunathanj9316]

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

[@UDiAudio]

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

[@akashmurthy]

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

[@eglenausedaite]

Awesome, Akash! You speak so clearly and interestingly.

[@rafilushan1988]

That's the best representation of sampling!

[@workethicrecords5901]

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

[@akashmurthy]

That's high praise! Thanks very much :)

[@CULTUM.mp3]

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

[@akashmurthy]

Cheers mate!

[@FirmanAsa]

The graphs and animations complement your explanation really well!

[@akashmurthy]

Thanks very much!

[@fahadzhossain]

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]

Thanks very much mate!

[@satbun477]

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

[@FreedomForKashmir]

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]

Thanks very much mate! :)

[@akira_rtt]

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

[@akashmurthy]

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

[@agustin2881]

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

[@akashmurthy]

Glad it helped mate!

[@MrSouzy]

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]

Great! I'm glad the graphics were useful.

[@amidall]

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]

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]

@@akashmurthy could you do a series on acoustics?

[@akashmurthy]

@@amidall any particular topics in acoustics?

[@CannedMan]

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.

[@Peaceful-er4vf]

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

[@akashmurthy]

Thank you so much for the support! :)

[@Apeskinny]

Man , that visualisation of aliasing is awesome!!

[@akashmurthy]

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

[@sriharinandan4981]

Dear Akash, I'm just an audiophile who loves music and keen to learn about it. Your videos are making me even more curious. You are an amazing teacher. 🙏. You have inspired me. Thank you

[@akashmurthy]

Thank you very much for the kind comment!

[@Margo-v2k]

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

[@akashmurthy]

Thanks mate!

[@jasdevsidhu9785]

Thanks!

[@akashmurthy]

Thank you! :)

[@ishaanpareek5751]

best video ever for audio processing

[@timoluetk]

This video series is seriously amazing!

[@akashmurthy]

Thanks very much mate!

[@shyamm4680]

Sampling theorem uses the keyword 'atleast' and we know that we cannot recover signal if we sample exactly at the Nyquist rate as discussed at 8:51. So shouldn't the theorem state that a band limited continuous time signal can be accurately converted to and from digital signal when sampled at a rate, 'more' than twice as high as the highest frequency component of the waveform? I have just replaced 'atleast' with 'more'

[@akashmurthy]

You're absolutely right. I cringe at it whenever I rewatch this video! It was a mistake.

[@shyamm4680]

Thank you for the clarification. Many don't realise this fact and use the expression fs>=2fmax conveniently. I would also like to thank you for the simplicity and quality of this educational video. Looking forward for more.

[@sumantnemmani4877]

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

[@akashmurthy]

Thanks for checking it out!

[@Apeskinny]

Love this! And the nod to Monty 😊👌

[@carlosa.chacon985]

I was going to write the exact same thing lol

[@mingzhou2213]

Hello, I didn't quite understand the part of leaving a buffer between required frequency and nyquist frequency: I understand that when converting digital signal back to analog signal, the low pass filter does not perfectly remove all undesired high frequency component, so we have a small portion of signal goes beyond the desired frequency. Whether setting the a buffer or not, this small portion of high frequency signal will always exist (Like for the buffer case you show at 18:56, there is a chunk in the buffer area). I can see that this region is distanced from the nyquist frequency. I don't understand why is it better, because in both scenario (desired signal frequency near 1/2 of sample rate or much lower than sample rate), we both have an undesired chunk.

[@akashmurthy]

@@mingzhou2213 Aliasing. I go into more detail on Aliasing in the next videos in the series. But you want to eliminate any frequencies beyong the nyquist, otherwise you run the risk of the the frequencies aliasing and being bounced back into the audible range of the signal. This happens because of the mathematical constraints of discrete signals in a digital system.

[@akashk961]

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

[@aashman]

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

[@aftofono]

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

[@akashmurthy]

I'm glad you discovered it now!

[@tim3.1415]

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

[@akashmurthy]

Thanks mate! :)

[@srinivasaprasanth]

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

[@akashmurthy]

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

[@BorisNienke]

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]

Glad you found it helpful, thanks!

[@piyushparashar8990]

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.

[@josuefox]

Excellent lesson, sometimes a little lost coz my english but mostly the visual helps. Just one point to explain, your experience at 8:21. a tone at 4kHz and a sample rate at 8KHz showing no waveform and producing no sound. Is it same event when the frequencies = sample rate ? ( for the same example , if we have a tone at 4Khz with a sample rate at 4Khz)

[@akashmurthy]

Thank you! So, trying to represent any frequency above the Nyquist will cause the signal to alias. You can check out video #4 Aliasing. But in essense, if you generate a 4kHz signal at a sample rate of 4kHz, the signal will be interpreted as 0Hz. So yes. It will be a very similar result as that of the Nyquist frequency(2kHz).

[@josuefox]

@@akashmurthy Yes I watched all now. Lot of infos in my brain, but the biggest discovery was about the fact that the sound is reproduced thanks to math and not directly by sample rate, as long as we respect the theorem. I have two questions if you have time. 1) There is a big discussion in a forum about converting samples. For example with kontakt libraries. They are taking a lot of space (by hundred of GB) , some people convert them to 16Bits and others thinking of even converting to 44.1Khz. I understand that the choice of sample rate and bit depth is more for the recording, but what about sample already digital ? My opinon would be to choose 44.1Khz (coz it's enough) and 24 bits just to avoid plugins "destructing the quality" ( I have read that plugins do that so better to have lot of bits ) and for the dynamic range which looks important. against clipping. 2) One of the explanation of Hi-res is that when you cut at 44.1KHz, you will lose harmonics , timbre and color of the sound. does it make sense ? thank you and sorry for the long msg

[@akashmurthy]

@@josuefox hey, thanks for the questions. Choosing bit depth is only a consideration when converting from analog to digital or from digital to analog. Changing the bit depth after a signal has already been sampled does not make a lot of sense. In DAWs, the sample values are represented as floating point values. Plugins use floating point calculations in 32 bit or 64 bits of precision. They rarely ever operate in 16/24 bit fixed point. And no, down sampling to a rate of 44.1kHz from something higher does not lead to loss of audible harmonics. But it does depend on the quality of the anti Aliasing filter that's doing the conversion.

[@josuefox]

@@akashmurthy Thank you so much for your answers.

[@huyhuynhquang3004]

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

[@akashmurthy]

Thanks so much!

[@CharvelIst]

May I ask what software you utilized for the sine wave animations? They're. quite brilliant...

[@ramseybolton1509]

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

[@akashmurthy]

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

[@danieliniguezv]

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

[@akashmurthy]

Thanks so much man! :)

[@ptsdon]

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

[@akashmurthy]

Thank you kind sir!

[@davidasher22]

Akash, you are in my brain right now!

[@akashmurthy]

Sorry to intrude 😅

[@tombrooks5118]

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]

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

[@happyBellaXD]

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

[@akashmurthy]

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

[@mekishethio8738]

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

[@akashmurthy]

You're welcome! :)

[@DAXBRWNMUSIC]

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

[@akashmurthy]

Thanks very much!

[@wilmercohen3764]

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

[@alwintheodoric6211]

truly a hidden gem!

[@exxzxxe]

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

[@akashmurthy]

Thanks mate!

[@RitwikKaikini]

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]

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!

[@tıbhendese]

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.

[@NISSIHYPERCORP]

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]

Thanks a mil for all the kindness!

[@HyperSlayer72]

I'm having a bit of trouble understanding stuff starting at 12:54 related to the intermediate analog signal. My current understanding is that the vertical components (lines) in the signal are essentially infinitely high in frequency, as thats the only thing that would explain how a analog wave could be perfectly vertical. As for the horizontal components they would be 0hz and have zero amplitude. Everything I just typed I would assume is wrong. Next, I understand the end goal is to find the single analog wave that serves as a solution to the intermediate analog signal by crossing each edge/point of the signal once. However I still don't understand how said solution is found. At 13:32 where you talk about discarding unwanted high frequencies from the intermediate analog signal I don't quite understand why this is done/how it aids in converting/solving the intermediate analog signal into a final analog signal. I thought the original digitally stored signal was already bandlimited in this example. Clearly i've gotten myself mixed up. Any guidance would be very appreciated.

[@akashmurthy]

Hey thanks for the question. It's quite interesting. So first question was, are there really signals with infinite frequency components, since the slope is 90 degrees? Well, I would blame the illustrations for this. At the intermediate signal stage, we're already in the analog (time) domain, so there is no instantaneous bit switching happening here. The signal is represent by analog components. And analog components are never ideal. Consider a capacitor. That's one of the components used to hold the state of the signal at some value for some period of time and then drop the value to a lower state or charge the value to reach a higher state. Here, charging and discharging a capacitor are not instantaneous operations. It's takes a bit of time. Very negligible, when compared to the audio rate, but still a deterministic amount of time. You get a ramp of values when the capacitor charges from 0v to 5v and a ramp of values when the capacitor discharges from 5v to 0v. You'd still have high frequencies because of these sharp ramps, but not infinitely high. The question about 0Hz DC components when the signal is held at the same state, well, that's interesting! I donno about this one. Maybe an electrical engineer could explain it. Those DC components would probably be there in the final audio signal, and would probably be stripped at the end by getting rid of any DC bias. Not sure.

[@akashmurthy]

And the second question, why is there a need to filter the signal, and how does that help in finding the final analog solution. Filtering is not a very intuitive process when viewed from the time domain. However, filtering is very intuitive when viewed from the frequency domain. A low pass filter will attenuate frequencies beyond a cut off, and we can see that vividly on a frequency vs amplitude graph. But these changes are harder to visualize on a time vs amplitude graph (time domain). How I try to build my intuition for this is by considering a square wave. A square wave has some fundamental frequency, and a lot of overtones. In the time domain, it looks like chunky repeating squares. And in the frequency domain, it looks like a ramp of values from the fundamental frequency, decreasing in amplitude all the way to the audible limit. Lets say, the task now is to find the fundamental frequency. If you put a low pass filter on it and crank it up, the lower the cut off frequency, the more and more this square wave sounds like a sine wave, and when you cut off all frequencies above the fundamental, it'll look and sound like a perfect sine wave. So, the jaggedy edged square wave was transformed into a smooth sine wave by the low pass filter. So low pass filtering can be thought to smooth out the time domain waveform, and the smoothed out points follow a sinc interpolation. Though the digital signal was band limited, the digital to analog conversion process inadvertently adds higher frequencies into the signal, because of the process we just discussed. So there is a need to put the low pass filter, and band limit the output analog signal.

[@HyperSlayer72]

​@@akashmurthy Ah, that makes sense regarding the natural speed limit of the capacitors themselves being tied to how high the frequency's are for vertical changes in amplitude. I needed to get my mindset out of the digital domain where bit switching would be nearly instantaneous.

[@HyperSlayer72]

@@akashmurthy If I follow you correctly here your relating the similar appearance of a square wave to that of an intermediate analog signal. No doubt they are visually similar, and I get what you mean with applying a low pass filter to smooth out the square wave. I'll stick to watching your series and if I feel like looking deeper into how a DAC functions I will do so after. Thank you so much for the detailed replies and the incredible video series!

[@baleeghal-baitar]

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]

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

[@johndoe-xf2ih]

Thank you so much for this tutorial man, I have a kinda stupid question, if the sine wave is a single frequency with no harmonics and is already band limited , why did the 3999 frequency cause aliasing when the sample rate was 8000 Hz when we dont even need a band limiter for this sine wave, is it because it was digital to analog?, because it was produced digitally so it would have an intermediate stage with high frequncies? , and if it was analog to digital would it still cause aliasing ? Again, sorry if its a stupid question but its been bugging me

[@Time-cc2qb]

These are amazing man

[@akashmurthy]

Thanks a lot man!

[@Rene_Christensen]

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]

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

[@Rene_Christensen]

@@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.

[@danieldeychakiwsky1928]

Great videos! Oddly though, while I can generate a 3999 Hz pure sine tone at an 8000 Hz sampling rate using Audacity, I'm unable to hear it when I play it back. I get the same time-domain pattern you do (~9:30 mins in). When I drop the pure town down to say 3800 Hz, I can hear it when I play it. Any ideas?

[@akashmurthy]

Cheers! I have little ideas I'm afraid. Could be different versions of Audacity? I'm running 2.4.2

[@Yogachara]

Excellent presentation. Your videos are so freaking good

[@akashmurthy]

Thanks a lot mate! :)

[@varunvenu88]

Amazing experience!! the engineering nyquist theorem is enlightening!

[@akashmurthy]

Hey I'm glad you found it useful!

[@upendraagnihotri2686]

Can you explain please ..what is the maximum representable frequency?T 11:19 TIMECODE

[@akashmurthy]

Sure. The maximum representable frequency here is the Nyquist frequency, which is half of the sample rate. So 22.05kHz is half of 44.1kHz and 5.51kHz is half of 11.025kHz. According to the Nyquist theorem, any frequencies above the Nyquist frequency cannot be accurately represented in the digital domain. So the maximum frequency you can have in your audio signal is 5.51kHz, if you are sampling at 11.025kHz . Any frequencies above that will cause aliasing.

[@upendraagnihotri2686]

Akash Murthy thank you dear.

Im trying to replicate this example of 3999Hz in the 4000Hz session but when I hit PLAY doesn't sound anything. ¿Do you know why can this be happening? Thanks for this information. Congratulations.

[@tails_the_god]

Hey question how would I set up my wav file when exporting NES audio to wav? Like the headers and stuff

[@mouhamadalmounayar2199]

I have a question , if we play the samples of a sound with double the original sampling rate, will we percieve any changes in the audio? According to your video , the answer seems to be no. Is that right?

[@danielolmos5484]

Great quality video, super helpful! Thank you

[@akashmurthy]

Cheers mate!

[@rainyafternoons7003]

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

[@akashmurthy]

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

[@howtoengineering257]

really super video ....but which software are u using for these animations ??

[@akashmurthy]

Thanks! I use Adobe After Effects for most of the animations. For some, I use Processing

[@gherbent]

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.

[@musicgpaul]

Thank you so much for these lectures!!

[@puspamadak]

Nice explanation! I have a question: If the filter would always smooth out the intermediate wave into a form of sine wave, how can we represent waveforms which are not sine waves? For example, what if we want the actual waveform to be a square wave which is just like the intermediate wave with no filtering?

[@akashmurthy]

Cheers! So, I've kept the illustrations simple and used sine wave here to represent the highest frequency that's getting retained from the filter smoothing out. Ideally, any rich complex sound can be decomposed into a set of sine waves. All observable sounds can be recreated by adding different sine waves of different frequency, amp and phase together. They are literally the building blocks of audio. You can think about a low pass filter as cutting off or "smoothing" beyond a certain frequency, any frequencies below that will not be affected. The same with square waves in your example. A square wave is just a harmonic combination of sine waves. If you apply a filter, you are cutting of frequencies above the threshold, but the frequencies below the threshold are untouched, so you still end up retaining all but the highest frequency components of the square wave. I'd suggest watching the video on Aliasing to understand this better.

[@puspamadak]

@@akashmurthy Thanks a lot sir, for clarifying my doubt.

[@SLigHtOfView]

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

[@akashmurthy]

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

[@__.daimon.__]

Excellent content. Great teaching. I'm curious as to where you studied & learned about this subject. Do you have recommendations for further study resources? Thanks for your work!

[@akashmurthy]

Thanks mate! I studied a master course on Audio Technology. But most of the videos from this series was developed through self study. The best resource that I found on these subjects was a book called Principles of Digital Audio by Ken Pohlmann. It's very dense and a bit difficult to understand at times, but it's a good resource.

[@__.daimon.__]

@@akashmurthy - Much appreciated! As others have said, you deserve a larger audience. The quality of work you've produced here is excellent. I'd like to learn more about DSP - & beyond that, about developing plugins with JUCE. I'll look-up the book recommendation... - thanks Akash.

[@ishykashy]

You are an amazing teacher. Thank you!

[@akashmurthy]

Thanks a lot mate!

[@jwfarknar]

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]

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]

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

[@sahandahmadzadeh5683]

thank you very much, you explained the concept very simple. perfect. and a question, how do you create your visualization parts? Is there any specific software you are using, I need to visualize my presentation, so your answer can be very helpful for me.

[@akashmurthy]

Thanks mate! I use Adobe After Effects for the animations

[@AyonAbeywickrama]

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

[@keveydaking]

Does this mean you believe 48 kHz to be too low of a sample rate if there it is less than 2.5x 20000 hz?

[@sarius2723]

Hey, this video is great. Can u give me your Sources? I want to use them for my Bachelor

[@akashmurthy]

Thanks! I updated the description to add the reference. It was basically a single book and a video on xiph.org

[@SAJAN_ECE]

Amazing video! Thanks for the efforts.

[@irethoronar34]

Crystal clear.

[@danieldnbt]

Bro your videos are so well done thank you

[@akashmurthy]

Thanks bro! :)

[@stefansoaremusic2699]

Awesome video mate thanks for the great work❤

[@akashmurthy]

Cheers mate!