Discussion Questions

What are you changing as you drag the sliders — the signals, or the rule that turns one into the other?
After Auto-fit, why do the same three numbers still work on an input signal they were never fitted to?
What would you have to store instead, if you wanted to reproduce the output without those three numbers?
Every output here is built from three copies of the input at fixed delays. What outputs could no choice of a, b and c produce?
Try to picture the input as a plain sine wave instead. Why would the three numbers be much harder to pin down?
Nobody told Auto-fit what the three numbers mean or what the rule is for. What is it given instead?

Where this shows up in 6.300

Lecture 1b - Signal Processing — a signal is a function that carries information
Homework - Transformations — shifting, scaling and reversing f(t): the copies this demo adds up
Homework - Transformations II — reading an output as a sum of two such copies, by eye

Input signal x(t)

This is what goes in.

every input here is built from copies of this one signal, f(t)

Output signal y(t)

blue = what should come out · orange = what your numbers produce

Learn the system (not the signal)

The signal on the left goes in. The blue signal on the right is what should come out. In between, three copies of the input — one delayed, one unchanged, one advanced — are each multiplied by a number and added together: y(t) = a·x(t−1) + b·x(t) + c·x(t+1). Set a, b and c so your output (orange) lands on the blue one. Auto-fit searches for them instead of you. New input sends a different signal through the numbers you already have.

a - weight on the delayed copy x(t-1)0.00

b - weight on the original x(t)0.00

c - weight on the advanced copy x(t+1)0.00