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HW #11 (due Thursday, April 26, 2001)
Problems 10.16, 11.3, 11.13ab, 11.25, 11.26abc in the text
Note (added 4/25/01):
Problem 11.13ab will not be graded; however, you should attempt
the problem anyway for practice.
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HW #10 (due Thursday, April 19, 2001)
Problems 9.13, 10.4ad, and 10.9abf in the text
Plus the following additional problem:
Two LTI discrete-time systems have the following impulse responses:
h1[n] = (1.2)n u[n]
and
h2[n] = (0.8)n u[n]
For each system:
a) Determine whether or not the system in causal.
b) Determine whether or not the system is stable.
c) Find the unit step response
(i.e., find y[n] when x[n] = u[n]).
Notes and Hints:
Prob. 10.9: The step response h[n] has non-zero values only
at n = 0, 1, 4, and 5.
Probs. 10.4 and 10.9: One approach to solving the problems
is to express h[n] as a sequence of impulse functions (as you
did in Prob. 9.20 in the last HW assignment). On the
other hand, some students may find it easier to use a
graphical approach.
Additional Prob., part b: Appendix C in your text may be helpful.
I will not be on campus Thursday, April 19. If you have
questions about the homework, please see me Wednesday or earlier.
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HW #9 (due Thursday, April 12, 2001)
The assignment is available via the following link:
HW #9 Assignment
You may assume that the sampled signal applied to the input of
the RC reconstruction filter is a sequence of weighted ideal
impulse functions.
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HW #8 (due Thursday, April 5, 2001)
Problems 6.23, 6.24, 9.1a, and 9.2b in the text
Notes:
Prob. 6.23: In part a, determine whether or not x(t) must be
bandlimited, and, if so, give a relationship between the maximum
frequency component of x(t) and T. In part b, give the type and
cut-off frequency/frequencies of the filter represented by
H(omega). In part d, look for a situation where aliasing gives
the same spectrum below 700 Hz as in part c.
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HW #7 (due Thursday, Mar. 22, 2001)
Problems 5.11, 5.19, 5.24 (give formula, but omit sketch), 5.26,
and 6.5 in the text
Notes:
Prob. 5.11: A trapezoidal pulse is equivalent to the convolution
of two rectangular pulses (you must determine the amplitudes and
widths). This is one approach; there are alternative approaches
for solving this problem.
Prob. 6.5: It is easier to determine the type of ideal filter this
circuit approximates if you plot the magnitude of the transfer
function. This takes some time, since the transfer function is
complex.
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HW #6 (due Thursday, Mar. 15, 2001)
Problems 4.10, 5.2, 5.3, and 5.5 in the text
Notes:
Prob. 4.10: Do not use the integral formula (4.23)
to find the coefficients.
Use Table 4.3 and the properties of Fourier series instead.
Prob. 4.10b: The width of the pulses in Figure P4.10b should be
1 second.
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HW #5 (due date extended again to Tuesday, Feb. 27, 2001)
Problems 3.18bcdf, 4.7cdeg, 4.8ace, and 4.9ace in the text
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[No homework due Thursday, Feb. 15, 2001]
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HW #4 (due Thursday, Feb. 8, 2001)
Problems 3.3, 3.4, and 3.5a-d in the text
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HW #3 (due Thursday, Feb. 1, 2001)
Problems 2.25acd, 2.26, 2.28, and 2.30abc in the text
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HW #2 (due Thursday, Jan. 25, 2001)
Problems 2.15, 2.18, 2.19, 2.20c, 2.22, and 2.24 in the text
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HW #1 (due Thursday, Jan. 18, 2001)
Problems 2.1 (parts a and b only), 2.2 (parts a and b only),
2.7, 2.8, 2.10, and 2.12 in the text
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