7/25/2019 periodic signals

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Homework 2 of EE110A

1) Is any of the following signals periodic:3ej(t+/2),3ej(t+/2)u(t),

k=[(t5k)+(t2

5k)]? If so, what is the (fundamental) period?

2) Express the real part of each of the following signals in the form Aeatcos(t + ) where

A, a, and are real numbers, A > 0 and < :4,

5ej/3cos(4t+ 3),

e2tsin(4t+/4), je(2+j200)t.

3) Consider a system with input x(t) and output y(t). For each of the following relation-

ships, determine whether the system is linear, causal, time-invariant, and/or stable: y(t) =

sin(x(t)), y(t) = ddtx(t), y(t) =t

tx()d, y(t) = x(t+2)+x(t2)2 .

4) Let x(t) =(t) + 3(t 2) 3(t 4) and h(t) = e2tu(t). Compute and sketch each ofthe following convolutions: x(t) h(t), x(t+ 3) h(t), x(t) h(t 4).

5) Let x(t) = u(t 2) u(t 6) and h(t) = e4tu(t). Determine y(t) = x(t) h(t) andg(t) =

ddt

x(t) h(t). How does y(t) relate to g(t)?

October 4, 2011 DRAFT