# Determining x(t) given a plot (Time reversal, expansion and shifting)

Discussion in 'Homework Help' started by jegues, Oct 15, 2012.

1. ### jegues Thread Starter Well-Known Member

Sep 13, 2010
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See first figure attached for problem statement.

See the 2nd figure attached for my work.

In part (b) it asks me to sketch the even portion of the original signal.

How do I know what that is?

I've sketched x(t) in my work and I know that the even portion of x(t) is,

$x_{e}(t) = \frac{1}{2}(x(t) + x(-t))$

but I can't simply describe x(t) for all values of t nicely. I can as I have in the figure, with different functional form for different values of t.

How do I do parts (b) and (c)?

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2. ### WBahn Moderator

Mar 31, 2012
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Your graph for x(t) looks fine, but your expression for it makes no sense.

Using your expression, what would x(t) be for t=-1, 0, 1, 2, 4, 5, and 10? Do those match the graph?

Are you supposed to express x(t) in terms of a piecewise definition or in a single expression using step functions? A single expression makes doing parts (b) and (c) much easier.

answer to part (a) looks good.