Digital Signal Processing Reference
In-Depth Information
(c)
(d)
(e)
(f)
x(t) = sinc(200t)
y(t) = 50 sinc
2
(50pt)
z(t) = 4e
-1000pt
u(t)
r(t) = rect[(t - 10
-3
)/2x10
-3
]
6.15.
(a)
Plot the ideally sampled signal and its frequency spectrum for the signal of Prob-
lem 6.14 (b) for sampling frequencies of 50, 100, and 200 Hz.
(b)
Discuss the suitability of these sampling frequencies for the ideal system.
(c)
Repeat Parts (a) and (b) for the signal of Problem 6.14 (d).
6.16.
The signal with the amplitude frequency spectrum shown in Figure P6.16 is to be sam-
pled with an ideal sampler.
(a)
Sketch the spectrum of the resulting signal for
ƒvƒ F 120p rad/s
when sampling
periods of 40, 50, and 100 ms are used.
(b)
Which of the sampling frequencies is acceptable for use if the signal is to be recon-
structed with an ideal low-pass filter?
X
[ ]
2
1
20
10
0
10
20
Figure P6.16
4p
3v
c
.
6.17.
The signal
f(t) = cos(v
c
t)
is sampled with an impulse train with period
T =
Find
and sketch the sampled spectrum.
v
v
c
6.18.
The signal with Fourier transform is sampled by three different im-
pulse trains with periods and Find and sketch the sampled
spectrum for each case. Which case or cases experience aliasing?
x(t)
X(v) = tri
1
2
p
v
c
, T
2
=
p
2v
c
,
2p
v
c
.
T
1
=
T
3
=
6.19.
The inverse Fourier transform of the signal in the previous example is
Find and sketch the sampled signals, using the sampling trains of the pre-
vious example
x(t)
=
v
c
2p
A
v
c
t
2
sinc
2
B
.
p
v
c
, T
2
=
p
2v
c
, and T
3
=
2p
v
c
A
B
T
1
=
.
Notice how aliasing appears in the
time domain.
6.20.
The Fourier transform
X(v)
of a signal
x(t)
appears in Figure P6.20. The signal
x(t)
N
(t) = x(t)p(t).
is sampled with an impulse train
p(t)
to form a new signal
The
P(v) = 4g
k=-
q
d(v - 4k).
Fourier transform of
p(t)
is
Sketch the Fourier trans-
form of
N
(t).
