DT Convolution-Simple Example Part 1

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Shows how to compute the discrete-time convolution of two simple waveforms.

This video is made available under the Creative Commons BY-SA license.

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Thanks, I had to do this for some test and could not understand the professor's explanation. This helped me a lot.

Coscos

Your video was the only one with any clarity on how this addition was done during the convolution. Thank you

ethanshuffel

Isn't that exciting? We got our first value here. Made me smile sooo wide :DDDD This video was so helpful!

FatimaRizvi-fb

Well, actually that won't be the case. If you have a signal x[n] and a signal x[n-2], then the -2 would account for moving to the right (or delaying the signal). Here you are working with x[-n] and x[-n-2], however, and x[-n-2] is nothing but x[n-2] flipped around the y-axis (because you just swap n with -n). So in this case, you are reflecting a signal shifted two to the *right* of x[n] (i.e. x[n-2]) around the y-axis, which results in a signal shifted two the *left* of x[-n] (i.e. x[-n-2).

tripplehop

Ok so people here are wondering about the shifting. In this video he is right when he does shifting to the left for h(-4-k). Here he mirrors/flips it first and then does the shifting. For the h(-4-k), if I do the shifting first, then I would move it to the right for -4 and then just flip it, HOWEVER if you mirror first then do the shifting you cannot move it the right for -4, you have to go to the left. If you don't believe me, you can do it. So the important thing to note here is either you do the shifting or scaling first. h(-4-k)=h(-(4+k))

marlborowaferchoco

I recommend to watch this video, its so informative.

khaledalhorani

Thank you. now I can clearly realize convolution

zaranikdel

uugh! I took a System Dynamics course and block diagrams jumped straight into the use of negative feedback and laplace transforms only. And that's natural after all, because control is all about constraint, and that's what negative feedback loops actually do. But then I started on my own doing MIT OCW 6.003 "Signals and Systems" to understand better how programs like MATALB might actually be doing the work and stuff and wow does that book (Oppenheim, et al 1996) waffle around in its examples. Impossible to follow. Diagrams nowhere near the text talking about them, going back and forth between the example and tangents.

There's a 2016 book, which is less problematic, but the structure is different, and just assumes students already know things like z-transform?

Your playlist here is a big help, especially this part where the convolution section is the worst section ever.

onlyAerik

look at it this way:

you invert the sequence x[n] which is centered at n = 0 and you get x[-n], then shift center to n = -3 or n+3 = 0. Then x[-n] becomes x[-(n+3)]. Hence, x[-n-3]. If you don't invert x[n] then you'll replace n by n+3 and get x[n+3]. So be careful about the - sign.

foonty

Won't deducting 4 move it to the right?

RsGhost

cheers darryl you have sorted me right out!

bigears

my prof wants it with 3 impulse responses.. any help? should i just do the first two, then the result with the 3rd?

MonkoGames

what if in the question x[n] and h[n] are given? should we consider them as x[k] and h[k] and follow the rest of the steps u told??

rishabhjain

Hi Darryl, in the 2nd term of the sum h(n-k) why does that not become h(n+k) when k is negative? For example when you calculate y(-2), here n = -2, then you would sum the products from k = -inf to k = +inf. There will be -k’s in that summation. For example x(-2)h(-2-(-2)) = x(-2)h(-2+2)? But that gives the wrong answer.

rchelipilot

thnx brouston, u jst saved my life! :)

miguelrodriguez

actually, x[-n-2] is x[-(n+2)] and is not equal to the flipped x(n-2), because in this case you shift to the right, because this is nothing but the signal x advanced (i.e shifted to the right ) and flipped about the 0 axis (or flipped and then shifted by 2 to the right if you want)

YaraOmran

At the very first place, why do we want to flip h[n] ? Is it not possible to make the convolution without fliping?

akmel

Not sure how there are 31 dislikes. Did ya'll come here for a Taylor Swift video or something? Great job.

lee_dubs

Please, could you tell me, why are you taking n=-4? Is there some rule for that?

jaratujemsam

you didn't explain that why do you start from. -4

nayakakshay

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