Discussion Questions

How long did each challenge take you by hand, and how long did Auto-fit take?
In the room recording, what pattern do the fitted weights follow? Where could it come from, given how the echo was made?
That system's copies are all delays, never advances. What would change if advances were allowed?
The 0.4 shift stops at a nonzero error. What would a system need in order to produce that output exactly?
Auto-fit is told nothing about what any of these systems is for. What is it given instead?
Where else might a system be specified by examples of its input and output, rather than by a formula?

Where this shows up in 6.300

Lecture 1b - Signal Processing — a signal is a function that carries information
Homework - Transformations II — reading an output as a sum of transformed copies, by eye

Input signal x(t)

The signal fed into the system.

Output signal y(t)

blue = target output · orange = your system's output

The system: one weight per shifted copy

Each stem is the weight on one shifted copy of the input. Click anywhere on the plot to set that weight.

Four systems to find

The same idea as the first demo, turned up. Each challenge gives you an input and a target output; in between, the system adds up shifted copies of the input, each with its own weight. Set them — sliders where there are three, a click on the stem plot where there are more — or press Auto-fit.

Challenge

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