Convolution Integral Example 01 - Convolution of Two Unit Step Functions

[@nurhaida1983]

I was shocked how simple it actually is when you explained. you went from the very foundation of the tau and finally combining. your explanation was crystal clear. thank you!

[@nando18224]

Convolution finally made sense after this video. Many thanks!

[@AdamPanagos]

Glad to hear that, thanks for watching!

[@septarap3901]

This is the kind of example they should demonstrate to show us how convolution works!! Thanks...!

[@juanr3strepo]

You just explained in 7 min what my teacher couldn't in 4 whole weeks. I'm so thankful for this video!

[@AdamPanagos]

Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam

[@atogh]

Wow thanks to You I finally get a reasonable explanation to convolution

[@AdamPanagos]

Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam

[@basmaeidarous16]

i cant believe how amazing this explanation is! ive been struggling with this for the past three weeks and noone has been able to explain it as well as you! my exam is tomorrow, honestly i owe you so much!

[@AdamPanagos]

Glad I could help! Thanks for watching and good luck on your exam!

[@soloboy2403]

He is explaining in a such simple way,i got it everything 👍🔥

[@УклетиХоланђанин]

^^ domo arigatoooo ** Give this man a medal!

[@ritesha8050]

wow. thanks a lot sir, this video just cleared a lot of my doubts

[@AdamPanagos]

Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam

[@shihaoshen2914]

sh1t bro thats really impressive and 100% amazing tbh, omg

[@AdamPanagos]

I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam

[@bennetbrooks1]

Easy to understand explanation of convolution.Thank you.

[@AdamPanagos]

You're welcome, glad to help. Thanks for watching.

[@himabinduvvaliveti9400]

beautiful and simple way of undertanding convolution. can u plz let me know the convolution of u(t) with u(-t)

[@BBoyTakeo]

Thanks, finally an understandable explanation of convolution!

[@AdamPanagos]

Glad I could help. Make sure to check out my website adampanagos.org for additional content that you might find helpful. Thanks, Adam

[@jd00d]

Finally makes sense, thanks Adam !

[@ericmonahan4095]

Great videos on convolution. I could not pick up the concept from my textbook. Everything is clicking now. Thank you.

[@samgarcia8348]

You are a beast in man form. Thank you for this.

[@MrHjld]

at 6:17, should y = t^2/2? Because it is the area under the line (integral)

[@AdamPanagos]

No.....the area under a line grows linearly....not to the 2nd order. Please watch the video again......

[@abebe7017]

You made my day! God bless you!

[@AdamPanagos]

Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content you might find helpful. Thanks, Adam

[@tudonghoabkhn]

Thank you very much, you explained it very easy :D

[@AdamPanagos]

Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam

[@koushiktutika90]

great work and how simple to under stand even im indian no difficulty in understanding thanks alot sir

[@AdamPanagos]

Glad to hear the video helped. Thanks for watching!

[@unona5876]

awesome, fearfully cool video

[@En3myDown27]

You are amazing! Thank you.

[@AdamPanagos]

Glad I could help, thanks for watching. If this video was helpful, make sure to checkout my website adampanagos.org where I have about 400 more videos.

[@anupamyedida5484]

I'm officially in love with your explanation ! Best tutorial on the topic. No bullshit , right to the point ! Love it ! :)

[@dorian-o6s]

Very clear, thank you!

[@AdamPanagos]

Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam

[@dlwalter]

Excellent explanation. Not much out there on convolution with step functions, which seem so common in signals applications. Any chance of making a video on auto/cross-correlation of signals in a similar manner?

[@solomonmolla436]

i learn a lot thanks for this video

[@sathvikgujjula9974]

can you do this in MatLab, please!! a video will be appreciated.

[@AdamPanagos]

I haven't done this particular example in Matlab, but here is a slightly different example that is worked in Matlab: kzbin.info/www/bejne/gouTop2Qmt96obM Hope that helps, Adam

[@joshuaaa3337]

sir, your explanation is fantastic, but i wanna ask you something. why you did not take case 3 from t to infinite?

[@AdamPanagos]

Case 1 handles t < 0. Case 2 handles t >=0. These 2 cases cover the entire t-axis, so there are now cases left. So, no need for a 3rd case. Hope that helps. Convolution takes some practice so consider watching the next few Convolution Integral Examples I have on the channel if you still need some more practice. Hope that helps, Adam

[@MultiHuze]

Lucid nice smooth and awesome explanation keep it up bro

[@AdamPanagos]

Thanks much, glad you enjoyed. Make sure to check out my website adampanagos.org where I have a lot of other resources available. Thanks, Adam.

[@raises4residents]

the case of t=0 shouldn't that be one and anything greater than that equal to t ....so shouldnt the piecewise function have three cases t less than zero=0 t=0 equals 1 and t greater than zero equal to t?

[@nb7359]

Very clear! this helped very much thank you!

[@AdamPanagos]

You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.

[@F2258]

Thank you Sir! Through this video,my concepts has been cleared.Now I'm able to solve the different problems of convolution.

[@AdamPanagos]

M Anas Excellent! Glad you found the video useful, thanks for the nice comment!

[@MichaelMatusowsky2010]

+Adam Panagos would you mind making an example where u(t) is convolved with a finite function (such as a square pulse of width 2 and height 1 for example)? Can't find any videos where a supposedly infinite function is convolved with a finite function.

[@AdamPanagos]

Michael Matusowsky That would be a great example, I'll add that to my "to-do" list. Unfortunately I'm not sure exactly when I'll get to it. At the moment I'm trying to prepare for the upcoming Spring semester. For the first time in a while I'm teaching a new class and I'm pretty swamped trying to get everything pulled together. Hopefully I can work through it and post in the coming days, stay tuned...

[@AdamPanagos]

+Michael Matusowsky Michael, I just made a video with the example you suggested. You can see it here: kzbin.info/www/bejne/qGWTi5etqMtkmtU Hope you enjoy. Thanks, Adam

[@MichaelMatusowsky2010]

+Adam Panagos thanks a lot, very much appreciated!

[@el-mehdibenchaib9950]

Thanks Adam.

[@AdamPanagos]

You’re welcome, thanks for watching. If you found the video useful make sure to check out my website (adampanagos.org) where I have a ton of other resources available. Thanks, Adam.

[@the_programming]

could u solve u(t+a)*u(t+a)

[@jeffreagan2001]

Really helpful for understanding convolution. What drawing software do you use for your videos?

[@AdamPanagos]

+bugman200001 I use an iPad app called Doceri (www.doceri.com) for most of my videos. This app lets you record all your handwriting ahead of time and use "breakpoints" to pause as needed. Once all the writing is down you can "play" the handwriting back while recording audio over it. I find this works much better than trying to write and talk at the same time. I'd definitely recommend checking out the app, I've found it very useful. Hope that helps!

[@wjrasmussen666]

which math class is this taught in?

[@AdamPanagos]

Very important in any undergraduate course in continuous-time signals and systems in engineering.

[@VanCDS]

On case 1 (4:30) shouldn't the integral upper limit be 0?

[@AdamPanagos]

***** If you like that upper limit better that's fine. In this particular case it really doesn't matter. The original limits are from -infinity to infinity. It turns out the function we're integrating over this interval is zero everywhere, so we get zero as the final integral answer. That being the case you can change the integral limits however you'd like and still get zero!

[@philipweber2253]

This is great, thank you for uploading

[@AdamPanagos]

Glad you found it useful, thanks.

[@kachupi6602]

This video is so helpful! Thanks

[@DeadHarryIsKl]

Amazing explanation, thanks!

[@AdamPanagos]

You're welcome, glad you liked the video!

[@lungofd]

Shouldn't the graph be shifted to the left when t > 0? Since u( t - tau ) can also be written as u( -tau + t), shouldn't that mean the graph is advanced by t for t > 0 , not delayed?

[@tekaaable]

No, just think of where u is zero and "switches off". t-tau=0 gives us tau=t , so u switches off at t

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[@t173hfl63]

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[@area51xi]

Why does u(-tau+t) shift leftward for t0. Aren't you evaluating earlier values of u(-tau) which would be a rightward shift?

[@AdamPanagos]

We're shifting the time-reversed signal u(-tau) so the normal convention/rule is reversed. In this case, it's easiest to keep track of where the unit step turns off. When the argument of u(t-tau) equal zero, is when t-tau = 0, when t = tau. So, as the value of t changes, where it turns of moves around. Hope that helps.

[@area51xi]

@@AdamPanagos Thank you. I think I can accept that now. Along these lines, I'm not entirely understanding the concept of the convolution integral using the variable t while the integrand has tau and dtau.

[@AdamPanagos]

@@area51xi The result of the convolution between two t-domain signals is another t-domain signal. The integral is performed for each value of t, over the variable of integration tau. So, you integrate out tau to yield t. You can use any variable you like for the integration variable; so you can let tau = alpha, beta, etc if that helps. So, pick a value of t, perform the tau integral. Pick another value of t, perform another tau integral. Compute the convolution integral for all values of t and you're done. Hope that helps.

[@johannschuur9673]

Beautiful! Thanks man

[@AdamPanagos]

You're welcome! Thanks for watching!

[@muhammadirfanbinjamilludin6665]

thanks..really helpful

[@techhelp4254]

Why is y(t) equal to t for t>=0 when in the drawing they only overlap for a brief period? Shouldn't y(t) = t be bounded by the domain of the overlap?

[@AdamPanagos]

+TechHelp The region of time that they overlap has length t and height one, so the integral of this area is t. As t increases, this region gets larger. Notice that the region itself has variable width t. So, this "brief period" is actually a variable amount of overlap and grows as t grows. Hence, y(t) = t. Hope that helps.

[@techhelp4254]

+Adam Panagos thank you, this makes sense!

[@AdamPanagos]

+TechHelp Great, glad to clarify!

[@AuroraClair]

Great explanation! Could you do a video of a convolution integral of some function (ex: f(t-tau)) and a delta function (delta (tau) an impulse function, when the value of this function is zero for all x, but x=0)? Integrating from 0 to t

[@AdamPanagos]

I don't have anything like that prepared at the moment but maybe I can get to it sometime in the future. In general, convolving with an impulse is pretty easy. Take the signal you're convolving with the impulse and simply place the time origin of the signal at the location of the impulse. For example, if you had a triangle signal symmetric about t = 0 and and impulse located at t = 5, the result of convolving these two signals would be a triangle signal at t = 5. This happens because the impulse function in the convolution integral essentially "sifts out" the underlying function at each point in time (e.g. repeated application of the sifting property of the impulse function).

[@AuroraClair]

I came to the same conclusion already after spending some time thinking about it, you're right! Thanks so much for taking the time and replying anyway! :) Great videos!

[@YoAirFresh]

Awesome. Thank you.

[@AdamPanagos]

You're welcome, thanks for watching.

[@Meshuggalo]

For the case of u(t - τ) where t

[@tcroyce8128]

the "tau" is the function variable whereas the "t" is a constant by which the signal is shifted. So lets consider a signal function x( tau - t). This is the standard way of representing a signal that has a "lag" in time by "t" units. ( the signal is considered to move from right to left across the t=0 mark as time goes by. ) Now if I need to flip the signal, the algebra rules is a bit weird ( you will see this mentioned in the oppenheim book ). We don't do this > x[ - (tau - t)] = x[ -tau + t]. This is WRONG. Here we are supposed to flip the signal but by the virtue of standard alzebra rules we also change the sign of the "shifting constant", ending up performing a invalid operation. We do this > x[ - (tau) - t ]. So to your specific request if a signal is such as > x [ tau + t], its shifted to the LEFT by "t" units. If the signal is > x [ tau - t] its the same signal shifted "t" to the RIGHT. x [ - tau + t] > flipped and shifted to the LEFT. x [ - tau - t] > flipped and shifted to the RIGHT. Flipping (also called mirroring ) and shifting are independent operations. I hope this clears up everything.

[@Edu888777]

Whats the real world application of this?

[@AdamPanagos]

The input and output of any continuous-time linear system are related via a convolution integral. So, any continuous time signal processing that ever occurs in a circuit is described by this convolution operation. That's just one of many ways convolution is "real world". Adam

[@Edu888777]

@@AdamPanagos Thank you

[@ibrahimalnafisi432]

Thanks!

[@AdamPanagos]

You're welcome, thanks for watching.

[@ElectricVideos]

Thanks

[@AdamPanagos]

+JonathanZ You're welcome, thanks for watching.

[@shahzadhashmi1454]

Brilliant..

[@smaillacoste9421]

شكرا merc thank u

[@AdamPanagos]

You’re welcome, thanks for watching. If you found the video useful make sure to check out my website (adampanagos.org) where I have a ton of other resources available. Thanks, Adam.

[@asaduzzamanjony6243]

impressive

[@omarbenmiloud4916]

hi i need help with fourier transform square exponential signal

[@mishelabramov1417]

thanks!

[@AdamPanagos]

You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.

[@ashishshinde3321]

nice

[@StSt1111]

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[@AdamPanagos]

I hope the video helped. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam

[@iamnew3360]

thank you

[@Lefachie]

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[@AdamPanagos]

Thanks, love some bagpipes! =)

[@LifeIsGood1992]

:)

[@PankajSingh-dc2qp]

how it 1 at t=0? I think it is 0 when t=0.

[@AdamPanagos]

No, the unit step function u(t) is 1 for t greater than and equal to zero. u(0) = 1.

[@TheAsimo1]

This is just awesome! Thanks a lot!

[@AdamPanagos]

You're welcome!

[@zekss07]

This is really helpful. Thank you!

[@AdamPanagos]

You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.

[@chinmaypujari4027]

Thank you

[@AdamPanagos]

You're welcome, thanks for watching!

[@genar8202]

thank you

[@AdamPanagos]

You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.