Response of an LTI System: Convolution

[@sm79165]

3:05 "We're going to use *a* instead of *tau* and by the time I'm done I want _everyone to be as confused as possible_ " you somehow managed to capture my feelings of distain for signals and systems and whoever diabolical person invented it and decided to not keep the variables consistent, with just that one sentence thank you

[@seandafny]

Have I finally reached a level beyond the scope of khan academy

[@balkey312]

extremely helpful. people like you that are getting me through my masters. thank you

[@TheComplicit]

"If you get this wrong you're in serious trouble" I actually LOL'd

[@DarrylMorrell]

@fingerboy18 The time constant is the amount of time it takes for an exponentially decaying signal to become smaller by a factor of e (to reach 0.3679 times its original value). In the signal x(t) = exp(-t/C), C is the time constant. The response of an LTI system is characterized by the poles of its transfer function; the time constant of a pole is the inverse of the real part of the pole. So the time constant of a system is the largest time constant of all of its poles.

[@DarrylMorrell]

@apparentlife22 The Fundamental idea is that x(t) is expressed as an integral (which is a limit of sums); Each term in the sum is a value x(tau) times a delta function which is shifted by tau. Because the system is linear, it operates on each delta function to produce the corresponding impulse response; the x(tau), since it is not a function of t, is a constant as it passes through the system.

[@nipunasudha]

Always listen to him in 1.5x speed :)

[@Edge9404]

1.25x makes him sound like a normal person.

[@RandyLott]

@DarrylMorrell Thank you Darryl. I've noticed that my textbook isn't very good at explaining the real world properties of systems, which is necessary for me to understand the topic. I appreciate the time and effort you've put in to help us.

[@circuithead94]

Hi there thanks for this a great video. Please can u provide me with the link to the video where u have dealt with the concept of x(t) = integral x(tau) delta(t-tau) dtau from - infinity to infinity. Thanks !!

[@Ensign_Cthulhu]

Sir, you give excellent, easy-to-follow explanations, but I think it would be very helpful to those in self-taught KZbin land if you gave links in your vids showing what to watch next (and possibly describing what we should have been watching just before). I feel like I'm skipping across your videos and missing a helpful linear progression.

[@eggrute]

Very easy to understand. Thank you for the video!

[@mnada72]

Extremely super helpful, thanks.

[@mauroprovatos]

@apparentlife22 it can become easier to understand if you look into convolution of a discrete time signal.

[@jacobvandijk6525]

Although mathematically CONVOLUTION looks like the sum (or integral) of a product (of two functions) giving you a number, it will "only" give you a third function (of t).

[@RandyLott]

I've watched many of your videos. I'm confused about the "time constants" of systems. My book has a problem that asks to find time constants, but the phrase is never mentioned in the chapter.

[@supaamazinazn]

Wow as an EE I am impressed... it's not easy to teach this stuff! My Fourier Analysis professor was joke compared to you... kudos!

[@abrahamhernandez3541]

Excellent Videos sir!

[@FTNomad]

I am glad how he is honest that the mathematics are so painful.

[@shikhasingh6865]

is convolution defined only for lti systems?if we have two non lti systems can we convolve them to get the output?

[@DearMajesty]

You are my savior.

[@DearMajesty]

Works great on 1.5x speed or if you're in a hurry 2x speed

[@5710fahad]

does convolution consider common area between the two signals or the total area between the two signals ??? Because from my knowledge of convolution it is the total area between the two signals at any instant of time...but while solving a GATE problem...i m nt able to get d answer... HELP plzzz...

[@colinhales1566]

It computes the area under the product of the 2 functions

[@irmaksaglam3782]

Thank you. " If i know the impuls response to a system, I can figure out output of that system if i put any input into it by just working convolutiopn integral." What does this mean?

[@DmK32625]

+Irmak Sağlam yani diyor ki eğer bir sisteme input olarak impulse'ı soktuğumuzda sistemin verdiği tepkiyi yani output'u yani h(t)'yi biliyorsak bu sistemin herhangi bir input fonksiyonuna verdiği tepkiyi de convolution integral'i kullanarak bulabiliriz. convolution integral formülünde geçen h(t-t0)'da sanırsam impulse fonksiyonundan dolayı geliyor. Yani impulse t=0'da değer verdiği için ve impulse'la bir fonksiyon çarpıldığında time shifting'ten ötürü fonksiyon delta(t-t0) ya da kısaca tao olarak gösterildiği için convolution'da da h'ı t-t0 olarak gösteriyorlar. sanırsam yani ben de çok emin değilim şimdi çalışmaya başlayacam.

[@yazanelmahmoud9947]

math def of the delta function ?

[@4thKyuubi]

Is this the Frequency response of LTI Systems? Is this H(omega)?

[@keespoort]

at 7.29 isn't it x(t)*h(t) instead of x(t)*y(t)?

[@keespoort]

nvmd... was taken care of

[@sarganarkaad2277]

“Black magic or voodoo....” , I guess we electrical engineers are all occultists

[@computo2000]

Great video!

[@mahakhan9762]

"smacking it with a hammer" sounds about right

[@LeonardoBritoVzla]

Great video!! thanks!!

[@joeLotfy]

7:00 you're damn right it is black magic. my final is in 2 days. I hope I don't fail my dad is gonna screw me lol

[@mehribaniasadi6027]

increasing of the speed was a great idea hahahaa thanks

[@sagarkhanal7613]

Thankyou!

[@mauroprovatos]

'whoops, and i did this wrong' . . 'argh'

[@yichizhang795]

thanks

[@mehribaniasadi6027]

the videos are amazing just the only small problem is that you talk to slow

[@samkowalski9879]

I want you

[@RubenVisawesome]

Might be the worst explanation I have ever seen.

[@Link1088]

Black magic, got it.

[@mehribaniasadi6027]

you talk too slow, I feel sleepy to follow you

[@qwerty.760]

use 1.25x speed :)

[@gaulovable]

Are you sleeping while making the tutorial?