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").

[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.

[Tobiasz]

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.

[isaroque]

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

[jtykgmi]

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

[bryandavis]

Great video this is way easier than the way I learned

[aokay]

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

[christerranaldo]

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

[karlchua]

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

[SwathiMenta]

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

[xoraxera]

Thank you so much! This was reallyyy helpfull!

[capo]

how would you multiply it, without a shift?

[sahilgoyal]

nice video...good job helped me a lot

[seaburyneucollins]

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!

[tanjuthechill]

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

[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.

[sdavid]

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?

[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

[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?