Digital Signal Processing Reference
In-Depth Information
0,
Æ=0
p
2
1,
Æ=
H(Æ) =
f
.
0,
Æ=p
Æ=
-
p
2
1,
Find an
h[n]
that satisfies these constraints. This is known as
frequency sampling
.
12.11.
Consider a discrete-time periodic function
x[n]
with DTFT
q
k=-
q
2p
4
a
2pk
4
2pk
4
X(Æ) =
X
0
b
d
a
Æ-
b
.
X
0
(
2pk
4
The values of
)
are
0,
k = 0
2pk
4
6,
k = 1
¢
≤
d
X
0
=
0,
k = 2
6,
k = 3.
Determine
x[n].
12.12
Find and plot the DTFT of
q
k=-
q
q
k=-
q
z[n] =
2d[n - 4k] +
d[n - 4k + 2].
12.13.
The signal
x(t) = rect[(t - 2)/4]
is shown in Figure P12.13.
(a)
Compute the four-point DFT of the signal when it is sampled with
T
s
= 2 ms.
Plot
the magnitude and phase spectra.
(b)
Use MATLAB to compute the eight-point DFT of the signal when it is sampled
with Plot the magnitude and phase spectra.
(c)
Use MATLAB to compute the 16-point DFT of the signal when it is sampled with
Plot the magnitude and phase spectra.
(d)
Compare the results of parts (a), (b), and (c). Comment on their relationship.
T
s
= 1 ms.
T
s
= 0.5 ms.
x
(
t
)
1
4
3
2
1
0
1
2
3
4
t
(ms)
Figure P12.13
12.14. (a)
Compute the eight-point DFT of the sequence shown in Figure P12.2(a)
(b)
Use MATLAB to confirm the results of part (a).
