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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
heck 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 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.
