Math Homework Assignment

I need this assignment completed by 2p EST.

 

For this assignment, you only have to do part A of each question, for 7 questions total.

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

Jason

Pedro

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.