Response of an LTI System: Convolution

Shows how the response of an LTI system to an arbitrary input is obtained as the convolution of the impulse response of the system with the input.

[sm]

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

[balkey]

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

[seandafny]

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

[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.

[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.

[eggrute]

Very easy to understand. Thank you for the video!

[circuithead]

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 YouTube 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.

[jacobvandijk]

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).

[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!

[mauroprovatos]

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

[FTNomad]

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

[DearMajesty]

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

[shikhasingh]

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

[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.

[keespoort]

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

[thKyuubi]

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

[irmaksaglam]

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?