Tutorial: Convolution sum

Learn about the discrete-time convolution sum of a linear time-invariant (LTI) system, and how to evaluate this sum to convolve two finite-length sequences.
CORRECTION: At 2:50, the graph heading on the right-hand stem plot should add "x[5]h[n-5]" ("h" instead of "delta").
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[@RoseHulmanOnline]

The method shown here is based on what physically happens with the system. Each input sample triggers its own scaled and shifted (delayed) impulse response, and these are all added together to form the output. Look particularly at 7:42, and you can see the effect of the delay in the argument for h, it appears as h[n-1]. The other method that you are thinking about ("flip and slide") is based on the convolution sum equation; the delay shows up as negated time index (k) and that's why h must flip.

[@Tobiasz931]

Thank you so much for those videos! I passed my exam only thanks to those (it's not really my field as I study IT)! It also helped a lot of my friends.

[@bryandavis2571]

Great video this is way easier than the way I learned

[@karlchua9188]

Taking my DSP Lectures this year and this helped me a lot! Too bad my professor cannot really explain this well. Thank you very much Rose-Hulman. Cheers from the Philippines

[@eggxecution]

currently studying for boards and understanding this for the first time I'm struggling 😂

[@sdavid78]

In the example at 6:00, h[n]={1,2,-1} with the second term underlined, indicating h[-1]=1 ; h[0]=2; h[1]=-1. Is it possible for the impuse response of a LTI system to be defined for negative n "h[-1]=1"? doesn't that mean to have a value for the impulse response prior to the impulse?

[@suyashmisra7406]

yes, such systems are called non causal systems. In practice, you can implement it if you use delays.

[@EssayWriting-h2c]

Thanks, I have been struggling to understand this concept but you made it easy !

[@nikoofayyaz8811]

thanks for the helpful video . just a question: what is the center if the number of h[n] is even?

[@tanjuthechill4871]

For given y(n) and h(n)
What will be input x(n)
??

[@christerranaldo906]

Thanks! Now that I have seen an example I understand it much better

[@morendav]

Is there a reason that you did not need to flip the LTI system (H) due to the negative sign infron of the k in h(n-k) ???
Please let me know as I am confused

[@RoseHulmanOnline]

Reply to Trần Hồng Phúc: The two formulas are equivalent: your equation (Xmax+Hmax) - (Xmin+Hmin)+1 = (Xmax-Xmin) + (Hmax-Hmin) +1 = (Xmax-Xmin+1) + (Hmax-Hmin+1) - 1 = Xlength + Ylength - 1 = equation in video.

[@isaroque1773]

OMG thank you so much for this vídeo. In 5 minutes I understood, in a much simpler way, the convolution summation. :D

[@seaburyneucollins688]

Wow, so this is what my textbook was trying to explain to me? I I regret spending so much time trying to decipher that load of gibberish, when I could have just watched this video instead!

[@tranhongphucdt]

Your tutorial is very understandable and usefull,but, your fomular for calculating the length of y is only right in this case, the others will be wrong. Could you take look again?

[@CoupedUpGenny]

how would you multiply it , without a shift?

[@YewJiaMing]

it was really easy to understand, besides, the method introduced in the example is really convenient.

[@tranhongphucdt]

Generally, the length of y =(max index x+max index h) - (min index x+min index h) +1

[@aokay720]

Thank you so much for taking the time to help me with this!

[@volkerblock]

right picture: delta or h [n-5] ?

[@RoseHulmanOnline]

h[n-5]... I caught this problem earlier and have the "CORRECTION" in the video description.

[@xMrJanuaryx]

I dont understand why its x[k]h[n-k] where does the -k come from why not +k?

[@xMrJanuaryx]

OH! Cause its a x(+k) if it were x(-k) then it would be h(n+k)!

[@SwathiMenta]

Amazing video! Was of tremendous help! Thank you :)

[@sahilgoyal1124]

nice video...good job helped me a lot

[@mcculloughmusprime]

Wow. Discrete convolution is a lot simpler than continuous.

[@andrewdavis6191]

elegant explanation! thank you

[@deathbypenguins]

This is a technique very different that what my professor taught us. A good shortcut, but I don't think my professor would be too impressed with it... Lol.

[@usmanhari7800]

This video solved my 1 year old problem

[@RoseHulmanOnline]

Good to hear!

[@williamidakwo2953]

Rose-Hulman Online same here. I am so grateful. Thanks

[@electrical4th371]

nice tutorial

[@xoraxera]

Thank you so much! This was reallyyy helpfull!

[@김뫄뫄-f2u]

감사합니다

[@al.qasimi]

Thank you so much

[@HarryXiVlog]

helps a lot! thx

[@killZtheterrannoob]

Thanks very useful XD

[@volkerblock]

good video, thank you

[@CreativeBangla]

Thank you so much. :)

[@deweymoorejr]

Very nice

[@harry4676]

Tks u

[@ArcaneKn1ght]

Chuck Norris is drawing this graphics.