Digital Signal Processing Reference
In-Depth Information
4.24
The impulse response of an LTIC system is given by
−
2
t
h
(
t
)
=
e
.
(a) Based on Eq. (4.54), calculate the transfer function
H
(
ω
) of the LTIC
system.
(b) The plot of magnitude
H
(
ω
)
with respect to
ω
gs referred to as the
magnitude spectrum of the LTIC system. Plot the magnitude spectrum
of the LTIC system for the range
−∞
∞
.
(c) Calculate the output response
y
(
t
) of the LTIC system if the impulse
train shown in Fig. P4.7 is applied as an input to the LTIC system.
<ω<
4.25
Repeat P4.24 for the following LTIC system:
−
2
t
−
4
t
]
u
(
t
)
,
h
(
t
)
=
[e
−
e
with the raised square wave function shown in Fig. P4.6(b) applied at the
input of the LTIC system.
4.26
Repeat P4.24 for the following LTIC system:
−
4
t
u
(
t
)
,
h
(
t
)
=
t
e
with the sawtooth wave function shown in Fig. P4.6(d) applied at the input
of the LTIC system.
4.27
Consider the following periodic functions represented as CTFS:
(i)
x
1
(
t
)
=
7
π
∞
1
2
m
+
1
sin[8
π
(2
m
+
1)
t
];
m
=
0
∞
1
4
m
+
1
cos[2
π
(4
m
+
1)
t
]
.
(a) Determine the fundamental period of
x
(
t
).
(b) Determine if
x
(
t
) is an even signal or an odd signal.
(c) Using the
ictfs.m
function provided in the CD, calculate and plot
the functions in the time interval
(ii)
x
2
(
t
)
=
1
.
5
+
m
=
0
−
1
≤
t
≤
1. [Hint: You may calcu-
1:0.01:1]. The M
ATLAB
“plot”
function will
give a smooth interpolated plot.]
(d) From the plot in step (c), determine the period of
x
(
t
). Does it match
your answer to part (a)?
late
x
(
t
) for
t
=
[
−
4.28
Using the M
ATLAB
function
ictfs.m
(provided in the CD), show
that the periodic function
f
(
t
) (shown in Fig. 4.10) considered in
Example 4.8, can be reconstructed from its trigonometric Fourier series
coefficients.
4.29
Using the M
ATLAB
function
ictfs.m
(provided in the CD), show that
the periodic function
g
(
t
) (shown in Fig. 4.11) considered in Example 4.9,
can be reconstructed from its trigonometric Fourier series coefficients.
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