Digital Signal Processing Reference
In-Depth Information
x[n] = 0.8
n
u[n]
(c)
Let and Solve for
y
[
n
] as a function of
n
.
(d)
Write a MATLAB program that solves for
y[-1] = 0.
y[n],
0
F
n
F
5,
using the form I
representation. Run this program to verify the results in part (c).
10.27.
Consider the MATLAB program for the simulation of an LTI system:
y(1)=0;
for n=1:6; x(n)=0.7^(n-1); end
for n=2:6
y(n)=0.9*y(n-1)+x(n)-x(n-1);
end
y
(a)
Write the system difference equation.
(b)
Draw the form I representation for the system.
(c)
Draw the form II representation for the system.
(d)
Express the input signal
x
[
n
] as a function of
n
.
(e)
Solve for
y
[
n
] as a function of
n
.
(f)
Verify the solution in part (e) by running the MATLAB program.
10.28.
For the system described by the MATLAB program of Problem 10.27,
(a)
Find the system difference equation.
(b)
Find the particular solution for the difference equation, with the excitation
x[n] = u[n].
(c)
Find the system transfer function.
(d)
Use the transfer function to verify the results of part (b).
(e)
Change the MATLAB program such that
x[n] = u[n].
(f)
Verify the solution in parts (b) and (d) by running the program. Recall that only
the steady-state response has been calculated.
10.29.
(a)
Find the transfer function for the difference equation
(b)
Use the transfer function to find the steady-state response of this system for the
excitation
(c)
Verify the calculations in part (b) using MATLAB.
(d)
Show that the response satisfies the system difference equation.
y[n] - 0.7y[n - 1] = x[n]
x[n] = cos(n) u[n].
10.30.
For each of the following problems, state the restriction on the variables
a
and
b
(if
any) that would be required for any sums to converge. If no restriction is needed, state
no restriction.
q
i = 4
b
i
(a)
a
-n
u[n]
*
b
n
u[n + 6]
(b)
(c)
(d)
a
n
u[-n]
*
b
n
u[-n - 6]
a
n
u[n - 3]
*
u[-n - 4]
