Digital Signal Processing EE 6360 Homework 2 Do not turn in the homework. Textbook Problems:

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Nov 24, 2013 (4 years and 7 months ago)

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Digital Signal
Processing EE

6360

Homework 2

Do not turn in the homework.

Te
xtbook Problems:

2.7 {b, d, j}, 2.10, 2.11,
2.16{b
-

6, 8,
11}, 2.17.b,
2.46 a,
2.52,
2.55, 2.62

(9 problems)

Special Problems:

10.

The input x(n) = {1,2,
-
1, γ} to an LTI sys
tem with an impulse response {1,α, β,2}
yields an output y(n) = {1,4,2,0,9,
-
4,4}. What is the output y
1
(n) of the LTI system
due to an input x
1
(n) = {1, 0,
-
1}?

^

11
. The following LCCDE describes the input
-
out
put relationship of a causal, LTI
system; determine the impulse response, h (n) of the LTI system.

y (n)

½ y (n
-
1) + ¼ y(n
-
2) = x(n)

¼ x(n
-
1)

12
.

The input to

a stable,
LTI system is given by x(n) = {
1

2 1} with a response

^

y

(n) = {
-
1
-
2
0

2 1}. Determine the output y1

(n) when the input

^

x1

(n)= { 1 2
3

2 1}.

^

13
.

An LTI system is described the following LCCDE:

y(n)

5/6 y(n
-
1) + 1/6 y(n
-
2) = x(n) n ≥ 0.

(a)

Find the zero
-
input, zero
-
state and the total s
olutions y
zi
(n), y
zs
n) and y(n),

when
x(n) = (1/5)
n

u(n), y(
-
1) = 6 and y(
-
2) = 25.

(b)

Find the total solution if the initial conditions are changed to y(
-
1) = 3 and

y(
-
2) = 12.5