EL6253 Linear Systems Midterm (03/23/2012) Solutions
Problem 1 Consider the system described by the following zerostate response
t+2
y (t) = S cfw_u(t) = exp(t)
u( 1) exp( 1)d
t 2
Determine whether the system is or is not (justify your answer):
a) zeros
EL625
Solution to Additional Homework 1
Let
1. u(k) = number of pairs of newborn minks purchased for introduction to the
farm at time k.
2. y(k) = number of pairs of 9monthold minks removed from the farm for pelt
production at time k.
3. xi (k ) = numbe
EL 625 Lecture 11
1
EL 625 Lecture 11
Frequencydomain analysis of discretetime systems
Theorem: If S is a xed linear discretetime system, the zerostate
response,
Scfw_z k = H(z)z k
(1)
Proof:
Scfw_z k =
Scfw_z k
k0
8
>
<
>
:

zk
cfw_z
H(z,k)
= H(z
Solutions to Problem Set 4
EL625
4.1
a) The current entering C(t) equals the rate of change of charge on C(t). Thus
dq(t)
d[C(t)vC (t)]
=
= C(t)vC (t) + C(t)vC (t) = iC (t).
dt
dt
Now
iC (t) =
v(t)
vC (t)
= v(t)
R2
vC (t)
C(t)vC (t)
=
C(t)
4
1
vC (t) +
v(