6:59 the left hand of that equation looks really suspicious though
@LuisLascanoValarezo Says:
Hard to watch these videoss..... I keep expecting a pun
@StEvUgnIn Says:
Its derivative is even weirder.
@Arnsteel634 Says:
I can’t tell if this is a comic book character video, comedy video, or math video
@jonahansen Says:
Dude - you could motivate the understanding of the convolution by showing it as the sum of the scaled impulse responses of the input at previous times. Would make a good figure.
@jonahansen Says:
Isn't a function. Engineers be like, "Whatever works".
@sebastiangudino9377 Says:
This is such a good video! It explains a weird topic so well! May i request a further video? You have probably some of the best videos on youtube about the laplace transform and now the impulse response. There is a logical next step in the form of transfer functions. They are the laplace transform of the impulse response, and they simplify the explicit formulation fot the time evolution of a system for a given input. But while algebraically i know how it works, it was a concept that never intuitively clicked. Maybe you are the one that can give some visual/graphical intuition to that weird set of operations?
@KenFullman Says:
Substituting a for various numbers I find that the function y=1/2a does NOT give a rectangle. It produces a symetrical graph consisting of two curves that meet at a=0, y=infinity. I don't understand where you got the rectangle from. So I'm out.
@shekarlakshmipathi Says:
I wish I can camp outside your house and listen to your lectures every day. This is awesome stuff. Thanks Zach.
@lforlight Says:
Matt Gray once made a video about a tunnel with insane reverberation. He also wanted to create the effect of talking in the tunnel while being anywhere else, so he made a video of a convolution for it. In the tunnel he took a recording of a cap gun go off, with the bang being virtually a delta function, and the following recording the response. Plugged that into a convolution in his audio software, and everything sounds like it happened in the tunnel.
Quite magical.
@JivanPal Says:
Ooh! Ooh! Now do Green's functions!
@Rene_Christensen Says:
I hope you are not breathin the air that relates to that particular 'air resistance'. The impulse response of that spring-mass system has no oscillation at all, so it must be sitting in oil or something ;-)
@cate9541 Says:
This is the first time i understood what people nean when they say math is beautiful
@LogicSammm Says:
Somehow I keep forgetting you have this channel😅
@VioletEverclear Says:
I was so confused for the first few seconds like “hold on, this voice isn’t meant to be on a math education vid” 😭
@highwaymen1237 Says:
Amazingly great video. Didn't realize I was also going to finally understand impluse function, convolution and the LTI control response. I wish my control class professor had said it this way.
@Aaravs21 Says:
Dirac delta is also used in quantum mechanics
@kacper9385 Says:
8:33, when taking derivative of the output side, the given result is considered to be for "t > 0" right? If not, how does one derivate the output? Thanks in advance <3
@Juanixtec Says:
While the functional and exact formulations of these kinds of fomulas and tools are extremely interesting. I have to point out that the most useful part of this is how wasy it is to plug them into computers and numerically calculate stuff with them. There will always be an error sure. But the fact that you can plug a whatever record of an impulse response and numerically convolve it with whatever signal to obtain the behaviour of the system is invaluable for simulation and signal processing.
@giovannifontanetto9604 Says:
In calculus 4 ( differential equations), when I saw the Dirac delta I was really asking myself if it was from the actual dirac, because he is basically a half god and lived so close to us in time. Could not believe we were gonna use something from him in an engineering course.
@Damian-sloos-climbing Says:
The ultimate function: x=0
@Henry14arsenal2007 Says:
So this is what the impulse response means in guitar amp cabinets.
@blackhole927 Says:
It feels wrong to hear this voice paired with educational content, and not some funny skit.
@thejourneyofgames9576 Says:
When did this guy start teaching people and make educational videos? I thought he was only a comedy guy. 🤔
@christophernodurft1868 Says:
When I learned about this in diff eq, I was so blown away by the brilliance. To be able to mathematically express impulse is just so genius because it ends up setting a system in motion but multiplying it by 1. Just brilliant.
@TheStillWalkin Says:
The convolution looks a lot like a crosscorrelation with time shifted function?
@kkgt6591 Says:
Why is there a need to flip the impulse response?
@themovercell2318 Says:
please make it factual, get a fact check
@excalibercuberdavid4681 Says:
I love direc delta because remembering that the inverse laplace of a constant is that constant multiplied by the direc delta function gave me 20 extra points on a Circuits 2 quiz
@DrHenrik Says:
its actually not a function (well unless you define it on hypereal numbers)
@kexcz8276 Says:
Bruh who uses delta V instead of a 😭
@gamerpedia1535 Says:
I want to mention that your rectangular formation of Dirac Delta function can be fudged to provide any value to the integral
Eg.
From -a -> a we have an area of n
This means our height would need to be n/2a
Take a -> ∞ and you get the same resuly, just with an area of n
@randycasty Says:
Currently learning this as an ee student and it definitely confused me at first
@SPY-ce8qf Says:
"Air resistance is accounted for" what is this blasphemy this is not a world I want to live in
@highgroundproductions8590 Says:
In math we call the "impulse response" a Green's function. We integrate the Green's function, and that's the convolution.
@guitarhero3812 Says:
As a computer engineering major, the delta function is something that still amazes me. The concept of an impulse response blew my mind when I first learned it; seeing its applications in things like filter design, digital signal processing, and even control systems. Also the fact that convolution in the time domain maps to multiplication in the frequency domain is something that still captivates me to this day.
@josgibbons6777 Says:
While several comments have already noted it's not a function (it's a distribution as well as a measure), it's worth knowing the true functions whose distributional limit is the Dirac delta are called nascent delta functions, in case you want to look up the rigorous details.
@haushofer100 Says:
The title is like " This cow is the weirdest human I've ever met".
@MH-sf6jz Says:
I like to think that Dirac delta function is the laplacian of the fundamental solution to the laplace equation.
@Teo-uw7mh Says:
its not a function
@NathanSimonGottemer Says:
TBF the Laplace Transform is still useful here because it turns out that convolution gets turned into multiplication in the frequency domain and also the FT and LT of the delta function are both 1
@graysonk6695 Says:
I like this one
@tayl9242 Says:
It is not a function
@dafta31 Says:
See Oppenheim… it wasn’t that hard
@shahriarrudra7495 Says:
😘🤩🤩🤩
@imbored1253 Says:
You just casually gave the best intuitive definition of convolution
@jtxx34xx Says:
The delta function also has a derivative. A good place to learn how to make sense of such "functions" (which are distributions, not functions) is Lieb & Loss's analysis book.
@LambOfDemyelination Says:
you could construe a function with an arbitrary area k by saying y=k/2a when x=0, then take the limit to say the Dirac delta function has area k under the graph.
point is, the area is undefined, and the function being "at infinity" is meaningless for real valued functions.
@whong09 Says:
Please cover laplace transform and fourier transforms too. This is where my eyes glazed over in my EE classes and I said fck it I'm switching to CS.
@AlexanderTheMiddle Says:
I literally have an exam on this tomorrow. I was watching youtube as a way of avoiding revision, but you fooled me into preparing for the exam!!!😤😤😤!! you!!!!!!! Thanks❤
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