Transformations II

The questions below are due on Thursday September 17, 2026; 02:00:00 PM.

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In Transformations you matched each single transformation of a signal f(t) to its plot. Real systems rarely apply just one operation — by linearity (superposition), a system's output is often a sum of transformed copies of the input. This exercise is about reading such a sum.

As before, let f(t) be the function of time t shown here:

For reference, here are the same eight transformations \textbf{A}–\textbf{H} from Transformations:

Each output below is the sum of exactly two of the transformations \textbf{A}–\textbf{H}. For each one, determine which two.

Hint: a step discontinuity in the output marks where a component's discontinuity lands; a value reaching \pm 2 means two copies overlap there.

Output g_1(t):

Two letters that sum to g_1 (e.g. AB):

Output g_2(t):

Two letters that sum to g_2 (e.g. AB):

Output g_3(t):

Two letters that sum to g_3 (e.g. AB):

Finding the two components by eye is a small version of a much bigger idea: given an input and a desired output, search for the combination of operations that produces it. When the combination has many terms and we let a computer do the searching, that is exactly learning a system — the subject of this week's optional companion demo.