I want to perform convolution for a sequence but instead of having the indices cycle from the ends periodically, I want to apply a function, specifically Abs
, to remap the indices.
Using ListConvolve
, what parameters and/or modifications to the inputs could allow this output?
For example, here is my specific case. My input sequences will have equal length. Using a summation, I can obtain the results I desire, but this runs in $O(n^2)$.
For an arbitrary sequence of length 5, this would be the convolution using summation.
Table[Sum[Subscript[a, j] Subscript[b, Abs[k - j] + 1], {j, 5}], {k, 5}]
b
? $\endgroup$ – mikado Jun 19 '16 at 10:19