Description
Problem 1
Find the z-transforms of the number sequences generated by sampling the following time functions every T
seconds, beginning at t = 0. Express these transforms in closed form.
(a) e(t) = exp(−at)
(b) e(t) = exp(−t + T)u(t − T)
(c) e(t) = exp(−t + 5T)u(t − 5T)
Hint: Note u(t) is the unit step function and exp(x) = ex
is the exponential function. First, you need
to obtain associated discrete functions (e[k] = e(T k)), and then you need to use the properties of the
z-transform that we discussed in the class.
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EECE 5610 Homework #2 Problem 2
Problem 2
A function e(t) is sampled, and the resultant sequence has the z-transform
E(z) = z − b
z
3 − cz2 + d
Find the z-transform of exp(akT)e(kT).
Hint: Solve this problem using E(z) and the properties of the z-transform.
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EECE 5610 Homework #2 Problem 3
Problem 3
For the number sequence {e(k)},
E(z) = z
(z − 1)2
,
(a) Apply the final-value theorem to E(z).
(b) Find the z-transform of e(k) = k(−1)k
.
(c) Explain how parts(a) and (b) are related?
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