ELEN3801  Fall 2009
Homework 3
Due Thursday October 1st at the beginning of class
(Mudd 227 9:10am)
1
Carefully justify ALL your answers
3.1  Let
f
(
t
) be a signal with energy
E
f
. Show that the energy of the signals

f
(
t
),
f
(

t
) and
f
(
t

T
) where
T
∈
R
is also
E
f
. What is the energy
of the signal
g
(
t
) =
cf
(
at

b
), where
a,b,c
∈
R
and
a
6
= 0?
(Hint: write
the energy integral for the various signals, and use a change of variables
to express it in terms of
E
f
)
3.2  Find and sketch
R
t
∞
f
(
x
)
dx
for the signals in panels (a) and (b) depicted
below.
(Hint: recall what is the area of a continuoustime impulse func
tion)
3.3  Consider the continuoustime systems below, described in terms of an in
put/output relationship, where the input is
f
(
t
) and the output is
y
(
t
).
Determine if the systems are linear or nonlinear.
(Justify your answer
fully, simply stating the answer will give you no credit)
(a)
dy
dt
(
t
) + 3
ty
(
t
) =
t
2
f
(
t
)
(b) 3
y
(
t
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 Spring '11
 KIM
 Signal Processing, discretetime systems, input/output relationship

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