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Intuitive Guide to Convolution – BetterExplained

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Like making engineering students squirm? Have them explain convolution and (if you're barbarous) the convolution theorem. They'll mutter something about sliding windows as they try to escape through one. Convolution is usually introduced with its formal definition: Yikes. Let's start without calculus: Convolution is fancy multiplication. Contents Imagine you manage a hospital treating patients with a single disease. You have: Question: How much medicine do you use each day? Well, that's just a quick multiplication: Multiplying the plan by the patient list gives the usage for the upcoming days: [3 6 9 12 15]. Everyday multiplication (3 x 4) means using the plan with a single day of patients: [3] * [4] = [12]. Let's say the disease mutates and requires a multi-day treatment. You create a new plan: Plan: [3 2 1] That means 3 units of the cure on the first day, 2 on the second, and 1 on the third. Ok. Given the same patient schedule [1 2 3 4 5], what's our medicine usage each day? Uh... sh

Like making engineering students squirm? Have them explain convolution and (if you're barbarous) the convolution theorem. They'll mutter something about sliding windows as they try to escape through one. Convolution is usually introduced with its formal definition: Yikes. Let's start without calculus: Convolution is fancy multiplication. Contents Part 1: Hospital Analogy Intuition For Convolution Interactive Demo Application: COVID Ventilator Usage Part 2: The Calculus Definition Part 3: Mathematical Properties of Convolution Convolution is commutative: f * g = g * f The integral of the convol

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