Digital Signal Processing Reference
In-Depth Information
R
2
Fig. B.1
Problem Q38
v
−
R
1
_
v
+
Y
R
+
+
+
X
C
Q40:
The signal x(t) = sinc(t - 5) is sampled with f
s
= 2 Hz. Plot the
magnitude spectrum of the digitized signal x(n). Is there aliasing? How
can we reconstruct x(t) from x(n)?
Q41:
Explain what frequency aliasing means.
x
ð
n
Þ¼f
2
;
3
;
4
g
and
Q42:
Find
the
convolution
of
the
two
signals:
y
ð
n
Þ¼f
1
;
5
g
.
Q43:
Explain the meaning of the DTFT and the DFT. How can we represent
digital systems and their I/O relationships in the time and the frequency
domains
using
these
transforms?
Which
transform
is
more
useful
in
practice?
Q44: Which is more general: the DFT or the ZT? How can we represent digital
systems and their I/O relationships using the ZT? How is the ZT related to
DTFT?
Q45: State the conditions in the time-domain that a system is BIBO stable. What
are the equivalent conditions in the z-domain?
Q46: What is the relationship between the s-plane and the z-plane?
Q47: Explain why the single-sided z-transform is sufficient for engineering
applications.
Q48: Explain why the digital subsystem H(z) = z
-1
represents a unit delay for
causal systems. How can we implement this system using digital hardware?
Q49: What is meant by the FFT?
Q50: Find the difference equation, the transfer function, the impulse response,
and the frequency response of the digital system shown in figure below,
noting that fs = 1 Hz. Is it FIR or IIR filter? LP or HP? What do you expect
the function of this system? Does it have an exact linear phase? Plot the
pole-zero diagram. Is the system stable?
Q51: a) What is the energy of the digital signal x(n) = 0.5 nT
s
u(n), knowing that
f
s
= 100 Hz? (Ans. 0.726 J) (Hint: use Tables for summation.)
Q52: What is the energy of the analog signal x(t) = 0.5 tu(t)? (Ans. 0.721 J)
Q53: How can we make the circular convolution of two finite digital sequences
x(n) (length N
1
) and h(n) (length N
2
) equal to their linear convolution?
Q54: State the advantages of DSP over ASP.
Q55:
Explain the function of the moving average digital filter. Is it FIR or IIR?
State a real-life application for this filter.
Q56:
Design a digital integrator. Is it FIR or IIR? LP or HP?
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