Unified Engineering II
Spring
2004
Problem S13 (Signals
and Systems)
In
class,
you learned about
a
smoother
, with
transfer
function
2
G
1
(
s
) =
−
a
(
s
−
a
)(
s
+
a
)
The
smoother
is
an example
of
a
lowpass filter
, which
means
that it tends
to
attenuate
highfrequency sine
waves,
but
“pass”
lowfrequency
sine waves. Unfortunately, the
smoother
is
noncausal,
which means
that
it can’t
be implemented
in
real time. A
similar
causal
lowpass
filter
is
2
a
G
2
(
s
) =
(
s
+
a
)
2
In
this problem,
you will
compare these two
lowpass
filters, to
see how
they
affect
sinusoidal
inputs.
Consider
an input signal
u
(
t
) =
cos
ωt
1. Find
the
transfer
function,
G
1
(
jω
), as
a
function
of frequency,
ω
.
2. Since
the
transfer
function is
complex, it can
be represented
as
G
1
(
jω
) =
A
1
(
ω
)
e
jφ
1
(
ω
)
where
the
amplitude
of
the
transfer function
is
A
1
(
ω
), and
the phase of the trasnfer
function is
φ
1
(
ω
).
Find
A
1
(
ω
) and
φ
1
(
ω
).
3. Find the
transfer
function,
G
2
(
jω
), as
a
function of frequency,
ω
, as
well as
A
2
(
ω
)
and
φ
2
(
ω
).
4. For
the
input
u
(
t
)
above,
show
that
the output of the system
G
1
is
y
1
(
t
) =
A
1
(
ω
) cos(
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '05
 MarkDrela
 Ω, Sine wave

Click to edit the document details