# Integrals, Unit Step, etc.

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Signals and Systems – Assignment 2

Complete the following parts and submit on 2/22/13 (Friday):

2.20 (c ) – (i), (iii), (v); 2.22; 2.23 & 2.24

Signals and Systems – Final Exam

Date Due: April 22, 2013, Monday @4:00 PM

Total = 100 points

Name:

Each question has three parts and each student will be answering the part of each question assigned to him as indicated below:

Part a

Part b

Part c

David

Marquidris

Jirreaubi

Question 1: Express the following complex numbers in polar form: (10 points)

a. 3 + j4 b. -100 + j46 c. -23 + j7

Question 2: Let Z1 = 7 + j5 and Z2 = -3 + j4.

Determine the following in both Cartesian and Polar form: (10 points)

a. Z1/Z2 b. Z1*Z2 c. (Z1-Z2)/(Z1+Z2)

Question 3: Classify the signals below as periodic or aperiodic. If periodic, then identify the period. (15 points)

a.

x(t) = cos(4t) + 2sin(8t) b. x(t) = 3cos(4t) + sin(πt) c. x(t) = cos(3πt) + 2cos(4πt)

Question 4: Determine if the following systems are time-invariant, linear, causal, and/or memoryless? (15 points)

a) dy/dt + 6 y(t) = 4 x(t) b) dy/dt + 4 y(t) = 2 x(t) c. y(t) = sin(x(t))

Question 5: Solve the following difference equations using recursion first by hand (for n=0 to n=4) and then plot. Check your solution using Maple or MATLAB (for n=0 to n=30). Attach plots to your solution. (20 points)

a) y[n] + 0.5y[n-1] = 2x[n-1]; x[n] = δ[n], y[-1] = 0

b. y[n] + 2y[n-1] = 2x[n-1]; x[n] = δ[n], y[-1] = 0

c) y[n] + 1.2y[n-1] + 0.32y[n-2] = x[n]-x[n-1]; x[n] = u[n], y[-2] = 1, y[-1]=2

Question 6. Solve the diﬀerential equations: (15 points)

a. x’’ + 4x’ + 13x = 0; x(0) = 3, x’(0) = 0

b. x’’ + 6x’ + 9x = 50 sin(t); x(0) = 1, x’(0) = 4

c. x’’ + 4x’ – 3x = 4et; x(0) = 1, x’(0) = -2

Question 7: Find the Fourier series of the function: (15 points)

a.

b.

c.

Signals and Systems

Final Exam

Date Due: April 22, 2013, Monday @4:00 PM

Total = 100 points

Name:

Each question has three parts and each student will be answering the part
of each question
assigned to him
as indicated
below:

Part a

Part b

Part c

David

Marquidris

Jirreaubi

Qu
estion 1
: Express

the following complex numbers in polar form:

(10 points)

a.

3 + j4

b.

100 + j46

c.

23 + j7

Question 2
: Let Z1 = 7 + j5 and Z2 =

3 + j4.

Determine the following in both Cartesian and Polar form:

(10 po
ints)

a.

Z1/Z2

b. Z1*Z2

c. (Z1

Z2)/(Z1+Z2)

Question 3
: Classify the signals belo
w as periodic or aperiodic. If periodic, then identify the period.

(1
5

points)

a.

x(t) = cos(4t) + 2sin(8t)

b. x(t) = 3cos(4t) + sin(πt)

c. x(t) = cos(3πt) + 2cos(4πt)

Question 4
: Determine if the following systems are time

invariant, linear, causal, and/or memoryless?

(1
5

po
ints)

a) dy/dt + 6 y(t) = 4 x(t)

b) dy/dt + 4 y(t) =
2 x(t)

c. y(t) = sin(x(t))

Question 5
: Solve the following difference equations using recursion first by hand (for n=0 to n=4
) and then plot.
C
Maple or
MATLAB (for n=0 to n=30).

(
20

points)

a) y[n] + 0.5y[n

1] = 2x[n

1]; x[n] = δ[n], y[

1] = 0

b.

y[n] + 2y[n

1] = 2x[n

1]; x[n] = δ[n], y[

1] = 0

c) y[n] + 1.2y[n

1] + 0.32y[n

2] = x[n]

x[n

1]; x[n] = u[n], y[

2] = 1, y[

1]=2

Question 6
.

Solve the di
?
erential equation
s
:

(15 points)

a.

x

+
4
x

+ 13x = 0
;

x(0) = 3, x

(0) = 0

b.

x

’ +
6
x

+ 9
x =
50 sin(t)
;

x(0) = 1
, x
’(0) =
4

c.

x

’ +
4
x

3x =
4e
t
;

x(0) =
1
, x
’(0) =

2

Question 7
:

Find the Fourier series of the function
: (15 points)

a.

b.

c.

Signals and Systems – Final Exam
Date Due: April 22, 2013, Monday @4:00 PM
Total = 100 points
Name:
Each question has three parts and each student will be answering the part of each question assigned to him
as indicated below:
Part a Part b Part c
David Marquidris Jirreaubi

Question 1: Express the following complex numbers in polar form: (10 points)
a. 3 + j4 b. -100 + j46 c. -23 + j7

Question 2: Let Z1 = 7 + j5 and Z2 = -3 + j4.
Determine the following in both Cartesian and Polar form: (10 points)

a. Z1/Z2 b. Z1*Z2 c. (Z1-Z2)/(Z1+Z2)

Question 3: Classify the signals below as periodic or aperiodic. If periodic, then identify the period. (15 points)
a. x(t) = cos(4t) + 2sin(8t) b. x(t) = 3cos(4t) + sin(πt) c. x(t) = cos(3πt) + 2cos(4πt)

Question 4: Determine if the following systems are time-invariant, linear, causal, and/or memoryless? (15 points)
a) dy/dt + 6 y(t) = 4 x(t) b) dy/dt + 4 y(t) = 2 x(t) c. y(t) = sin(x(t))

Question 5: Solve the following difference equations using recursion first by hand (for n=0 to n=4) and then plot.
Check your solution using Maple or MATLAB (for n=0 to n=30). Attach plots to your solution. (20 points)
a) y[n] + 0.5y[n-1] = 2x[n-1]; x[n] = δ[n], y[-1] = 0
b. y[n] + 2y[n-1] = 2x[n-1]; x[n] = δ[n], y[-1] = 0
c) y[n] + 1.2y[n-1] + 0.32y[n-2] = x[n]-x[n-1]; x[n] = u[n], y[-2] = 1, y[-1]=2

Question 6. Solve the di?erential equations: (15 points)

a. x’’ + 4x’ + 13x = 0; x(0) = 3, x’(0) = 0
b. x’’ + 6x’ + 9x = 50 sin(t); x(0) = 1, x’(0) = 4
c. x’’ + 4x’ – 3x =
4e
t
; x(0) = 1, x’(0) = -2

Question 7: Find the Fourier series of the function: (15 points)

a.

b.

c.