Convolution equation explained simply in 3 forms: discrete, continuous and matrix-vector

Explaining the mathematics of convolution visually in three ways
Understanding a Toeplitz and circulant matrix

[rd-tkjs]

Excellent explanation, very comprehensive and complete, thanks !

[DavidVonR]

Thank you!!! I'm finally understanding convolutions! I first encountered convolutions when I studied Laplace transforms, but I didn't know they had such wide application.

[scramah]

Thank you for the video: maybe I am misunderstanding, but your indexing scheme seems inconsistent. You use 0 to denote the first element in the f column vector but you use 1 to denote the first element in the g column. Not sure if that was intentional or not. At 16:25 you say that, "The output is affected immediately", which would suggest that your indexing scheme should maintain the definition of how to index the first element across all vectors. Cheers~

[jimmea]

I came up with a matrix-vector convolution kernel which is similar to yours except instead of flipping and shifting the matrix rows right, it flips the vector and shifts the matrix rows to the left descending. I suppose both methods work though, yours is just more intuitive