Problem 1:
1.1) What is the result of:
a) a+b
b) a*b
c) a.*b where ‘a’ and ‘b’ are column vectors
1.2) Repeat 1.1 but with ‘a’ as a matrix
Turn in your answer.
Problem 2:
Plot following functions in the same plot (overlay)
𝑦1 = cos(𝑡) 𝑦2 = sin(𝑡)
where ‘t’ is a vector from 0 to 50 with the increasing step:
a) 1
b) 0.01
Do the signals look smoother when we reduce the increasing step? Turn in your answer, plots, and codes.
Problem 3:
Write a program to solve the system of equations of three variables using the matrix inverse method. The program should include user prompt to input equation coefficients. The general form of a three-variable equation is 𝑎𝑥 + 𝑏𝑦 + 𝑐𝑧 = 𝑑. Assume that the users have to give the coefficients in the order ‘a’, ‘b’, ‘c’, and ‘d’. Test your program with the following system of equations:
2𝑥 + 3𝑦 + 𝑧 = 3
𝑥 + 3𝑦 − 𝑧 = 6
2𝑥 + 2𝑦 = 7
Turn in your code and result from the Matlab command window.
Hints: Note that from Linear Algebra theory, you can solve the system of equations using matrix inverse method by the following steps:
Step 1: Rearrange the equations so that all of them have the form of 𝑎𝑥 + 𝑏𝑦 + 𝑐𝑧 = 𝑑
Step 2: Write the equations in matrix form 𝐴 ∗ 𝑡 = 𝑏
Step 3: The result is 𝑡 = 𝐴−1 ∗ 𝑏
𝐴−1 is the inverse matrix of A and could be computed in Matlab by using the command inv(A).
Problem 4:
Write an M-file program to calculate:
where ‘log’ is the natural logarithm function, ‘sign’ is the signum function.
The program must include a user prompt to input the parameter ‘µ’ and input ‘x’. Note that ‘x’ can be either a scalar number or a vector. The above equation shows the input-output characteristic of a µ-law compressor used in pulse-code modulation (PCM).
Test your program by plotting ‘y’ according to ‘x’. Let µ=255 and ‘x’ is a vector changing from 0 to 1 with the increasing step 0.01. Turn in your code and plot. Keep a copy of your code, you will need it later.
