#commutativity

Question 1: Single choice

mediumAI-checkedConvolutional Neural Networks

The discrete convolution of two sequences is $(f * g)(i) = \sum_a f(a)\, g(i - a)$ , where $a$ runs over all integers. Which substitution shows in one step that $f * g = g * f$ ?

$b = a - i$ , which turns the sum into $\sum_b f(b + i)\, g(-b)$ 1
$b = i + a$ , which turns the sum into $\sum_b f(b - i)\, g(2i - b)$ 2
$b = -a$ , which turns the sum into $\sum_b f(-b)\, g(i + b)$ 3
$b = i - a$ , which turns the sum into $\sum_b g(b)\, f(i - b)$ 4

Timed test