Signals and Systems - Convolution theory and example

Zach with UConn HKN presents a video explain the theory behind the infamous continuous time convolution while also presenting an example.

[@augustoalmeida2586]

it so nice to see tyrion lannister moving up in the present world! cheers ma friend!..

[@HD-dw7zk]

hahaha

[@maxtobias6034]

You prolly dont give a damn but does anyone know a method to get back into an Instagram account..? I somehow lost the password. I love any tips you can offer me.

[@chrisjude9933]

@Max Tobias instablaster :)

[@coreyhulse8226]

21:48 the real MVP

[@OswaldChisala]

Prior to his fix, I felt like a kid with OCD as I focused on the mistake Instead of the lecture haha. He's the real MVP fasho :)

[@The_Handy_Man]

Finally understand this for my exam. Thank you!

[@williamtsang8723]

Great presentation to answer the questions of why and how to do convolution!

[@jadecutter1760]

Thank you so much!! That was a wonderful breakdown of concept and the math process. The dude in the jacket showing up was hilarious too, broke the tension of all that math for a bit lol.

[@deshengwang3364]

Thanks, I have seen so many videos about this theme, this is one of the best introductions on the theme of convolution!!!!!!!!!!!!!!!!

[@klktudicr]

Watching this video in a quiet/dark room. 21:48 scared the crap out of me! Great video!

[@jayjayf9699]

That horrific music at the beginning near took my ear off

[@jacobvandijk6525]

The man is an engineer, not a great designer of videos. But you're right, it's terrible.

[@veljko100able]

watch at 1.25x speed

[@cucumcumber]

at 16:39 when 0

[@digathomas]

yes

[@geetarthjugtawat7355]

Haha I spotted the same thing

[@yarenkaya7872]

Thank you for this beneficial tutorial, sir! Plots made me interpret a bit more readily.

[@manethdulshan9449]

loved it Very first time learning Convolution theory Felt so nice and time went without even noticing

[@syz911]

The second part of the integration (for t > 1) can be done much easily by breaking simply into 0

[@KansasFashion]

So man, First question, I wonder can we do convolution to more than two functions? Second, I have a project, for now, I want to put a chirp inside of a song and detect this chirp in the song in the matlab. Should I use anything involved with convolution? Or should I use Fourier format? Please let me know!

[@yarenkaya7872]

For your first question, convolution has an associativity property; therefore, you can convolve the functions in the order you want.

[@morrisombiro]

One of the better videos on convolution !!

[@jjdavidian]

What about the reverse problem consisting of determining the channel's input response h[t] knowing x[t] and y[t] measurements

[@iSuL6aNoo]

you are awesome man, this is good example. I think you should have explained more in how you get the t-1

[@zedlepplin9450]

yea

[@Mulkek]

Thanks, and explain so clearly!

[@AhmadTalkss]

at 13:10, isnt the t supposed to shift to left cuz ( -Tau + t )

[@donovanvaughan7161]

at 16:15 when you give the answer to the integral, should it not be 2(e^(-t) +t -1) instead? exponent of e would be -t as opposed to -tau edit: I see this small slip has been addressed a few times already. Excellent video over all that I'm grateful to have for free.

[@glaurung78]

the "slip" is not so "small". The whole time, he is supposedly trying to find y(t), the output of the system as a function of time. Then he gives an answer containing τ and t. This is not a calculation error, which can happen sometimes -- it does not even make sense.

[@dickaroundmark2111]

yeah

[@gecovasttt]

great video,very useful, where can i find other example of continuous time-convolution? I really need for the class

[@ItIsYourBoyMe]

Thank you very much! Great video!

[@ueiwqoak]

Why do the taus that are part of the solutions to the individual integrals (like for t between 0 to 1) change to ts when we are presented with the final piecewise solution?

[@GooogleGoglee]

Isaac Howenstine I'm happy I was not the one to saw it.. I was getting very confused.

[@merdenyesil559]

Thanks you for good explanation. I have a one question. ramp function t or -t ?? You say t but I think -t.

[@demographicreplacement539]

how did he do the integral at 16:50? someone please help

[@NoobMaster-yw6eo]

Am having issues on how to break up the integration into multiple parts, like where do i start where do I finish, if someone illustrate that part for me it will be very helpful.

[@jakeyoung3117]

Around 8:50 when he graphed X(t), should it have been shifted to the left side of the vertical axis?

[@phymath-jisanislam9639]

yeah.

[@xlmentx]

Yup

[@Ilias259]

from 09:59 he uses the correctly shifted version.

[@babatundetaiwo2817]

x(t-T) would be a right shift in tau then a reflection wouldn't it?

[@bruceliu9808]

thanks sir, all respect

[@user-qo4hz8pf5r]

was it a cameraman (22:00). Who popped up and fixed the mistake? :)

[@ayakhateeb6399]

I have some questions about this can help me??

[@dd-iu6iy]

Nice explanation sir

[@lazraqaziz9262]

At time 16:44 for t between 1 and t replace tout by t on the final integral

[@OceanNoire]

I am wondering how accurate you draw straight lines :)

[@Matias-be5bi]

Great video

[@guruprasad7587]

using partial fractions problems pettandi sir degree final year vi

[@Hadkek]

Is he just writing all this stuff backwards on the glass wall so we can see it? That's impressive

[@satyajitsarkar1645]

Hadkek he wrote it normally and then flipped the image in post

[@kaih6361]

He is a leftie. No, he is not. this is like convolution flipping.

[@sartazaziz856]

Thank you.

[@absalomalila493]

awesome

[@TheSharke1995]

16:30 to inform you my brother the final result must be in term of t only so it must be e^t. the rest are correct

[@user-mn8th3ie1t]

You're right.

[@InventionClass]

How it is possible? You write in this way such as conventional for us but mirror image for you. Great %%%

[@dhavishsinghbissessur5004]

He’s writing the same way for himself as well lol, that’s an inverting mirror.

[@humoodatoo]

Thank you

[@chandragupta2828]

thanks

[@Feptick]

aight this is messing with my brain, is he left-handed or is that just the camera's flip view thingy

[@sebastianfigueroa9550]

How do you make these videos reflected?

[@janeknox3036]

I will give you a hint: the vast majority of these teachers appear to be lefthanded.

[@infinteuniverse]

What? He confused the shit out of me when he's explaining how to find the convolution of h(t)=2e^-2x and the x(t) he came up with. When t is less than zero, h(t) will go to infinity, not zero, how can the convolution give zero for values of t less than zero?

[@LyCaNid]

It is the product of h(tau) and x(tau) that is zero. Not h(tau) itself. I see why it might be confusing, but I also think he forgot to mention that for those inputs he uses all function values for tau < 0 are 0. They are causal inputs. So h(tau) follows: 2*e^-tau tau >= 0 0 tau < 0

[@zacfubar1]

Lycanid is correct. We should have explicitly used multiplication by the unit step function in the descriptions of x(t) and h(t), which would make both functions 0 for t

[@DzmitryLazerka]

You should've drawn the final result chart.

[@UConnHKN]

We wanted to show the process more than the result. A graph of the output may be nice, but in this example I believe it would not show any intuitive representation of the convolution process. Also, the graph is a bit difficult to draw accurately as it is not a standard function. For these reasons, we thought it best to not graph the output. - Andrew

[@wym247]

Arigatou

[@KoltPenny]

Danny Rand keepin' it real.

[@commissargamer]

Is he writing in reverse order

[@andreapaolamyleneblanca7345]

ily

[@ankurverma3638]

he looks like the guy from game of thrones lmao

[@ueiwqoak]

Is it me or does he confuse t and tau a lot? I'm getting confused

[@UConnHKN]

Were sorry for your confusion, the use of tau here is only a dummy variable. As you can see in the definition of convolution, the tau is integrated out. The tau is simply used to represent the function variable as we slide the "input" in time. I hope this helps! -Andrew

[@okktok]

Actually, x(t) is not discontinuous

[@zepsiman6421]

Boris Kramer

[@joeLotfy]

yup, that's it, im failing this final.

[@payasotrompeiros8944]

μεγαλος μαγκας

[@KangJangkrik]

I have no idea how he teach us while writing in "mirrored" way, that's tough 😂

[@KangJangkrik]

@Levi Skioury hmm smart enough

[@crimsonfist1408]

flipping and shifting makes nosense to me. seems arbitrary

[@crimsonfist1408]

wait I think I get it.. its (-tau + t)

[@adamalhaje2024]

intro is so loud

[@user-bp8yd7uy6h]

LOL he sound like Ben Shapiro in 2x

[@klong4128]

Since I aready fully understand what is CONVOLUTION . I agree with Your explaination . I SEE 10% FULLY DO NOT KNOW what You are talking about since They are the ABSOLUTE beginner ! I doubt whether 90% understand what You are talking ? without blurr? To Inprove Your teaching ,You should use MOVING PICTURE INSTEAD of STATIC-SNAP SHOT PICTURE ! GOOD try to explain what is CONVOLUTION ! keep it up !

[@ebarbie5016]

Solving such simple convolution graphicaly is a total waste of time! Just use the step function to define the piecewise function and then calculate the conv integral analytically. It took me 20 seconds exactly...

[@eno-obongudoka290]

It’s done though so students can understand how to think in the course not just solving mindlessly. It’s made easy so students can easily pick it up.

[@zionbaker1815]

Is there an example online of someone using that method?

[@jacobvandijk6525]

Right, this (5:07) is the end of this video for me. Bye.

[@zey3340]

would be a better video if you just stopped playing with those damn pencils bro.

[@aakashdewangan7313]

First of all remove that noise in the video beginning...that was irritating... someone wants to study and you are playing this noise in the beginning of your video....

[@matvw49]

is this guy for real ? At 16:18 he gave the result for an integration over tau and this result still contains tau (his integration variable). Seriously ?? And he even checked it on his so-called calculation that he did beforehand... Does this guy have a degree or teaches grad students ? I hope not....

[@UConnHKN]

We apologize for this small error. The variable in question should obviously be a ``t'' not a ``tau''. We do these videos in as few takes as possible so that continuity is preserved. Zac is a wonderfully smart man and even the best of us make mistakes. We believe that his explanation of the Convolution theory and worked example is superb, useful, and far outshines the small error in notation. ~Andrew

[@eglintonflats]

Another goof who spits out what he memorized by rote.

[@UConnHKN]

Were sorry if there is a problem with our explanation. I assure you that we work very hard on these videos and that those presenting them are qualified to do so. We may prepare solutions beforehand to keep the videos short (as you can see, they get very long) and we are all humans who make mistakes from time to time. If there is something we can do to improve how we present this information, please let us know. We are always open to advice and criticism.

[@Hooriyafahad609]

if he would have memorized it then he would never had made a mistake.his approach is clear .the only bad thing was he made some careless human mistakes

[@MA-qz1sd]

Be thankful for other people’s effort. This is free material don’t be a douche