Response of an LTI System: Convolution

Comments · 46

• SE

  @seandafny · 8 years ago

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

  43

• SM

  @sm79165 · 3 years ago (edited)

  <a href="https://www.youtube.com/watch?v=p_gLEDYLUeU&amp;t=185">3:05</a> &quot;We&apos;re going to use <b>a</b> instead of <b>tau</b> and by the time I&apos;m done I want <i>everyone to be as confused as possible</i> &quot; <br>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

  5

• TH

  @TheComplicit · 9 years ago

  &quot;If you get this wrong you&apos;re in serious trouble&quot; I actually LOL&apos;d

  5

• FT

  @FTNomad · 14 years ago

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

• RA

  @RandyLott · 14 years ago

  @DarrylMorrell Thank you Darryl. &nbsp;I&apos;ve noticed that my textbook isn&apos;t very good at explaining the real world properties of systems, which is necessary for me to understand the topic. &nbsp;I appreciate the time and effort you&apos;ve put in to help us.

• EN

  @Ensign_Cthulhu · 13 years ago

  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&apos;m skipping across your videos and missing a helpful linear progression.

  5

• EG

  @eggrute · 5 years ago

  Very easy to understand. Thank you for the video!

• JA

  @jacobvandijk6525 · 5 years ago (edited)

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

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• DE

  @DearMajesty · 9 years ago

  Works great on 1.5x speed or if you&apos;re in a hurry 2x speed

  3

• MN

  @mnada72 · 5 years ago

  Extremely super helpful, &nbsp;thanks.

• DA

  @DarrylMorrell · 14 years ago

  @fingerboy18 The time constant is the amount of time it takes for an exponentially decaying signal to become smaller by a factor of e &nbsp;(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.

• DA

  @DarrylMorrell · 15 years ago

  @apparentlife22 The Fundamental idea is that x(t) is expressed as an integral (which is a limit of sums); &nbsp;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.