Question

I would like convolve a discrete signal with a discrete filter. The signal and filter is sequences of float in F#.

The only way I can figure out how to do it is with two nested for loops and a mutable array to store the result, but it does not feel very functional.

Here is how I would do it non-functional:

conv = double[len(signal) + len(filter) - 1]
for i = 1 to len(signal)
  for j = 1 to len(filter)
    conv[i + j] = conv[i + j] + signal(i) * filter(len(filter) - j) 

Answer 1

Try this function:

let convolute signal filter =
    [|0 .. Array.length signal + Array.length filter - 1|] |> Array.map (fun i ->
        [|0 .. i|] |> Array.sum_by (fun j -> signal.[i] * filter.[Array.length filter - (i - j) - 1]))

It’s probably not the nicest function solution, but it should do the job. I doubt there exists a purely functional solution that will match the imperative one for speed however.

Hope that helps.

Note: The function is currently untested (though I’ve confirmed it compiles). Let me know if it doesn’t quite do what it should. Also, observe that the i and j variables do not refer to the same things as is your original post.