Digital Signal Processing Reference
In-Depth Information
Q17:
State Parseval's theorem for periodic and non-periodic analog signals and
define the power and energy spectra and spectral densities.
Q18:
Explain why the single-sided Laplace transform is sufficient for engineering
applications.
Q19:
From the basic definition, find the Laplace transform and its ROC for the
signal x(t) = exp(t)u(t).
Q20:
Plot the pole-zero diagram of the system H(s) = s(s + 1)/
[(s2+5s + 6)(s + 5)]. Is the system stable? Justify your answer.
Q21:
What is the sample space of the die tossing experiment? How can we
represent outcomes of this experiment using a random variable? Is this
random variable continuous or discrete? Plot the pdf of this random variable.
Q22:
Two dies are tossed. What is the probability that the first is 1 and the second
is 6?
Q23:
Explain the physical meaning of the statistical mean and variance of a
random variable.
Q24:
Plot and find the mean and the variance of the following Gaussian pdf
p
ð
x
Þ¼
1
p
e
x
2
.
Q25: Two Gaussian noise processes n
1
(t) and n
2
(t), where the first has more
power than the second. Approximately plot the pdf's of the two noise
random variables. Are n
1
and n
2
energy or power signals?
Q26: Find the mean and variance of the random signal x(t) = sin(wt)+n(t),
where n(t) is Gaussian noise with variance = 0.1.
Q27:
State the Wiener-Kinchin theorem for WSS random signals.
Q28:
Define the autocorrelation function of a random variable X(t).
Q29:
Explain the meaning of white noise. What is the effect of an ideal LPF on
the correlation between white noise samples?
Q30:
Outline the principle of a matched filter. State an application for matched
filters in binary communications (Plot the block diagram).
Q31:
Show that the matched filter is essentially a correlator.
Q32:
Show that the ideal analog LPF is a non-causal system. How can we modify
this theoretical system to be practically realizable?
Q33:
What are the advantages of active filters over passive filters?
Q34:
What is the importance of impedance matching between successive stages
of an electrical system? How can we attain this aim when designing analog
passive filters?
Q35:
What does the 3-dB point of a filter mean?
Q36:
If a sixth-order analog BPF is required, what is the order of the prototype
normalized LPF? Why?
Q37:
Find the transfer function and draw the circuit diagram of a second-order
Butterworth
f
c
= 50 Hz,
maximum
gain
LPF
with
cutoff
frequency
G
m
= 1, and RL = 10 X.
Q38:
What is the function of the following circuit? Find the transfer function and
plot approximately its magnitude frequency response (Fig.
B.1
).
Q39:
What does uniform sampling mean?
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