Melody Caron
EE2170-L01 Fall 2010
9/14/2010
EE2170
Design and Analysis of Signals and Systems Laboratory
Lab 2: Matrix Construction, Operations and Manipulation in Matlab and Basic
Signal Operations
A. Objective
The purpose of this lab is to become familiar with matrix operations and commands
in Matlab and to understand basic signal operations.
B. Procedure
I. Part I: Matrix Construction, Operations and Manipulation in Matlab
1. Define two variables x and y which have the values -2 and 3, respectively. Then
use the command window to perform the following operations:
a. x2+y2
x^2+y^3
ans= 31
b. x/(x+y2)
x/(x+y^2)
ans = -0.2857
c. log10((2/5) y)
log10(2/5*y)
ans = 0.0792
2
d. |y| +2x
sqrt(abs(y))+2*x^2
ans= 9.7321
e. sin(x/8)
sin(pi*x/8)
ans= -0.7071
f. |x+jy|
abs(x+y*j)
ans= 3.6056
jtan-1(1)
g. e
exp(j*atan(1))
ans = 0.7071 + 0.7071i
2. Define two arrays A and B as:
A = [1 4 2], B = [2 3 4; -3 2 5; 2 4 2]
a. Find the average value of the elements of A using the formula
Here, N is equal to the number of elements in the vector A.
sum(A)/3
ans= 2.3333
.
b. Find the mean value of all the elements in the second column of B.
sum(B(:,2))/3
ans= 3
c. Create a matrix S (with the same size as B) whose elements are equal to the
square of the corresponding elements in B.
Melody Caron
EE2170-L01 Fall 2010
9/14/2010
S=B.^2
S=
4 9 16
9 4 25
4 16 4
d. Calculate the matrix operation of A x B.
A*B
ans= -6 19 28
e. Attempt to evaluate ATB and report what appears on the command
window. Explain?
??? Undefined function or variable 'T'.
“T” is an undefined variable at this point, and it cannot be used in matrix
operations until it has been defined.
3. Using “randn” command, produce 100 samples normally distributed, and store
them in the 1x100 array C.
a. Find the maximum and minimum elements of C.
max(C);min(C)
ans= 3.5784; -2.9443
b. Find the standard deviation and variance of all the elements of array
D = 2xC.
std(D);var(D)
ans= 2.3248; 5.4047
c. Find the product of all the elements of C.
prod(C)
ans= -7.3221e-023
II. Part II: Basic Signal Operations
1. First click on the “Basic Signal Operations” applet. Practice using the various
controls on this applet. What happens when you adjust the amplitude slider?
When you adjust the amplitude slider, the amplitude of the selected function
increases or decreases accordingly
2. Describe what happens when you adjust the time shift slider on any of the
signals x(t).
When you adjust the time shift slider, the signal x(t) shifts left or right along
the x axis (time) in the same direction that you move the slider.
3. Repeat #2 when the time shift slider is applied to the signal x(-t).
When you apply a time shift to the signal x(-t), the signals shifts along the x
axis in the opposite direction that you move the time shift slider.
Melody Caron
EE2170-L01 Fall 2010
9/14/2010
4. Plot the signal x(t) = u(t) and y(t) = u(t). The signal u(t) is the unit step
function. Next, plot 3x(t – 2) + 3y(-t – 2).
x(t) = u(t), y(t) = u(t)
3x(t-2)+3y(-t-2)
5. Use the controls on the applet to demonstrate that if y(t) = rect(t – 0.5, 1), then
y(-t + 1) = y(t).
y(t) = rect(t-0.5, 1)
y(-t+1) = y(t)
6. If x(t) = u(t) and y(t) = rect(t – 0.5, 1), plot the graph of x(t + 1) + y(-t + 2).
x(t+1) + y(-t+2)
7. If x(t) = rect(t – 0.5, 1), then plot the graph of rect(t, 1).
Melody Caron
EE2170-L01 Fall 2010
9/14/2010
x(t) = rect(t, 1)
8. Plot the graph of the product exp(-t)u(t)sin(8t). To better understand what is
happening mathematically, try filling in the following table (the values can be
obtained by positioning the mouse over the graph of each signal, at which time
the signal coordinates will turn red):
t
-3
2.5
-2
1.5
-1
0.5
0
0.5
1
1.5
2
2.5
exp(t)u(t)
0
0
sin(8t)
0
-0.9
exp(t)u(t)sin(8t)
0
0
0
0
0.3
0.5
0
0
0
0
-1
0.8
0
0
1
0.6
0.36
0.22
0.13
0.08
0
-0.7
0.98
-0.5
-0.2
0.91
0
-0.4
0.32
-0.1
0.03
0.07
Melody Caron
EE2170-L01 Fall 2010
9/14/2010
exp(-t)u(t)sin(8t)
9. Now bring up the applet called “Sinusoids”. Plot the signals cos(4t) and sin(4t).
cos(4t) and sin(4t)
10. Find the smallest positive phase shift, f, such that sin(4t – f) = cos(4t). Insert a
plot in your write-up which confirms your answer.
Melody Caron
t
-3
-2
-1
0
1
2
3
EE2170-L01 Fall 2010
cos(4t) = sin(4t -1.5)
f = 1.5
cos(4t)
0.84
-0.15
-0.65
1
-0.65
-0.15
-0.84
9/14/2010
sin(4t-1.5)
0.84
-0.15
-0.65
1
-0.65
-0.15
-0.84
11. Explain the difference between a phase shift and a time shift in a sinusoidal
signal.
Phase shift is used only when describing sinusoidal signals. Time shift is used
when describing the shift of any signal, periodic or non-periodic. The term
“phase shift” implies that the signal is periodic and its “phase” has been shifted,
thus it is in a different phase of the same periodic signal. For example, in the last
question I demonstrated that cos(4t) = sin(4t -1.5). The signal when the signal
sin(4t) undergoes a phase shift of 1.5, it is in the same “phase” as cos(4t) and is
therefore equal.
C. Conclusion
Through the execution of this lab, I learned how to create matrices in Matlab and
perform essential matrix operations. I also discovered some basic properties of signals
and signal operations using the specified Java Applet. These skills will be essential to
completing more complex labs in the future.