To calculate the total medicine usage, line up the patients and walk them through the rooms: Monday There's no rooms afterwards, and your treatment is done. On the last day, you walk into room #3 and get 1 unit. The next day, you walk into room #2 and get 2 units. On your first day, you walk into the first room and get 3 units of medicine. Next, imagine we have 3 separate rooms where we apply the proper dose: Rooms 3 2 1 How can we organize this calculation?Īn idea: imagine flipping the patient list, so the first patient is on the right: Start of line The patients are overlapping and it's hard to track. On Wednesday, it's trickier: The Monday gal finishes (1 unit, her last day), the Tuesday people get 2 units (2 * 2), and there are 3 new Wednesday people.On Tuesday, the Monday gal gets 2 units (her second day), but two new patients arrive, who get 3 each (2 * 3 = 6).Given the same patient schedule, what's our medicine usage each day? That means 3 units of the cure on the first day, 2 on the second, and 1 on the third. Let's say the disease mutates and requires a multi-day treatment. Everyday multiplication ( 3 x 4) means using the plan with a single day of patients: * =. Multiplying the plan by the patient list gives the usage for the upcoming days. Question: How much medicine do you use each day? Well, that's just a quick multiplication: Plan * Patients = Daily Usage A list of patients: Your patient count for the week (1 person Monday, 2 people on Tuesday, etc.).A treatment plan: Every patient gets 3 units of the cure on their first day.Imagine you manage a hospital treating patients with a single disease. Part 4: Convolution Theorem & The Fourier Transform.Convolution is commutative: f * g = g * f.
Part 3: Mathematical Properties of Convolution.
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