Digital Signal Processing Reference
In-Depth Information
(a) By sketching the magnitude spectrum of each of the LTIC systems,
comment on the frequency properties of the two systems. Classify
the two systems as a lowpass, highpass, bandpass, or an allpass fil-
ter. Recall that a lowpass filter blocks high-frequency components; a
highpass filter blocks low-frequency components; a bandpass filters
blocks frequency components within a certain band of frequencies;
while an allpass filters allows all frequency components to be passed
on to the output.
(b) Determine the impulse response for each of the two LTIC systems.
5.32
Sketch the gain and phase responses for the three LTIC systems given
below:
(a)
h
1
(
t
)
=
2
t
e
−
t
u
(
t
);
(b)
h
2
(
t
)
=
u
(
t
);
(c)
h
3
(
t
)
=−
2
δ
(
t
)
+
5e
−
2
t
u
(
t
)
.
For each of the three systems, show that the input signal
x
(
t
)
=
cos
t
produces the same output response. How can this result be explained?
5.33
(M
ATLAB
exercise) By making modifications to the
myctft
function
listed in Section 5.10, sketch the magnitude and phase spectra of the
following signals:
(i)
x
1
(
t
)
=
sin(5
π
t
) for
−
2
≤
t
≤
2 with sampling rate
ω
s
=
200
π
samples/s;
(ii)
x
2
(
t
)
=
sin(8
π
t
)
+
sin(20
π
t
) for
−
1.25
≤
t
≤
1.25 with sampling
rate
ω
s
=
1000
π
samples/s.
5.34
(M
ATLAB
exercise) Compute the CTFTs of the CT functions specified
in Problem 5.1. By plotting the magnitude and phase spectra, compare
your computed result with the analytical expressions listed in Tables 5.2
and 5.3.
5.35
(M
ATLAB
exercise) Compute the output response
y
(
t
) for Problem 5.29
by computing the CTFT for
x
(
t
) and
h
(
t
), multiplying the CTFTs and
then taking the inverse CTFT of the result.
5.36
(M
ATLAB
exercise) Sketch the magnitude and phase Bode plots for the
LTIC systems specified in Problems 5.20 and 5.21.
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