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Problem Set
7
1
ECSE304 Signals and Systems 2
Fall Semester 20
11
McGill University
Department of Electrical and Computer Engineering
Problem Set
7
Distributed:
Monday,
March 28
, 20
11
Due
:
Thursday, April 7
, 20
11
Assignments can be worked in Groups of 2. A cover sheet, which is found at the bottom
of the Assignments page in the ECSE304 webCT site, should be handed in with each
assignment.
MatLab Exercises
In all MatLab Exercises, you are to show all your work and hand in both your MatLab
code and the plots that you generate.
Functions in MatLab for State Space Representations
The
lsim
MatLab function takes a system described by statespace equations and runs a
simulation of the system using arbitrary inputs and initial conditions. The command
lsim
(A,B,C,D,U,T,X0)
plots the time response of the linear system:
x
Ax Bu
y
Cx Du
=
+
=+
±
That is, the differential equation is integrated from time T(0) to T(length(T)), starting at
the initial condition X0 and using the input U. The input vector must have the same
number of entries as the time vector.
If the initial conditions are all zero, X0 can be
omitted.
The
ss2tf
MatLab function takes a set of statespace equations and converts them to
the equivalent transfer function. This is done using the command
[num,den] =
ss2tf
(A,B,C,D,iu)
. This command creates the numerator and
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 Spring '09
 JANBAJCSY

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