Unified Engineering II
Spring
2004
Problem S15 (Signals
and Systems)
Find
the
Fourier
transforms
of
the following
signals:
1.
g
(
t
) =
δ
(
t
−
T
)
Note:
The
system
with impulse response
g
(
t
)
produces
an
output that
is
the
input
delayed by
T
.
Since
delays
occur frequently
in
signal processing,
G
(
jω
)
is
an
important
transfer
function.
2.
�
1
,
t
g
(
t
) =
  ≤
T
0
,

t

>
T
Note:
Because
g
(
t
)
is
symmetric,
G
(
jω
) should
be real.
Please express
your
answer
so that
it
is
apparent
that
the answer is
real.
3.
1
g
(
t
) =
t
2
+
T
2
Hint:
If
you find the
integral hard
to
do, you
might be able to
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 Fall '05
 MarkDrela
 Digital Signal Processing, LTI system theory, important transfer function

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