## Description

ECES-352

Lab #1: Introduction to Matlab

Pre-Lab: You should read the Pre-Lab section of the lab and go over all exercises in

this section before going to your assigned lab session.

Verification: The Warm-up section of each lab must be completed during your

assigned Lab time, and the steps marked Instructor Verification must also be signed

off during the lab time. The laboratory instructor must verify the appropriate steps

by signing on the Instructor Verification line. When you have completed a step that

requires verification, simply raise your hand and demonstrate the step to the

instructor. Turn in the completed verification sheet to your instructor when you

leave the lab.

Lab Report: It is only necessary to turn in Section 3 as this week’s lab report with

graphs and explanations. You are asked to label the axes of your plots and include a

title for every plot. In order to keep track of plots, include your plot inlined within

your report.

Forgeries and plagiarism are a violation of the honor code and will be referred to

the Dean of Students for disciplinary action. You are allowed to discuss lab exercises

with other students and you are allowed to consult old lab reports but the submitted

work should be original and it should be your own work. In particular, any MATLAB

code that you submit should be your own, the words in your report should be your

own, and any plots that you submit should be your own.

Due Date: The Verification part is due today, and the lab report will due on next

week at the start of your lab.

1 Pre-Lab

In this first week, the Pre-Lab will be extremely short and very easy. We will be testing out your ability to

do a WebCT on-line quiz, and also some other software for doing the grading. Therefore, make sure that

you read through the information below prior to coming to lab.

1.1 Overview

MATLAB will be used extensively in all the labs. The primary goal of this lab is to familiarize yourself

with using MATLAB. Please read Appendix B: Programming in MATLAB for an overview. Here are three

specific goals for this lab:

1. Learn basic MATLAB commands and syntax, including the help system.

2. Write and edit your own script files in MATLAB, and run them as commands.

3. Learn a little about advanced programming techniques for MATLAB, i.e., vectorization.

1.2 Movies: MATLAB Tutorials

On the Web-CT course page, there are a large number of Real-media movies on basic topics in MATLAB,

e.g., colon operator, indexing, functions, etc. Look for the link with the movie film icon.

1.3 Getting Started

After logging in, you can start MATLAB by double-clicking on a MATLAB icon, typing matlab in a terminal window, or by selecting MATLAB from a menu such as the START menu under Windows-95/98/NT.

The following steps will introduce you to MATLAB.

(a) View the MATLAB introduction by typing intro at the MATLAB prompt. This short introduction

will demonstrate some of the basics of using MATLAB.

(b) Run the MATLAB help desk by typing helpdesk. The help desk provides a hypertext interface to the

MATLAB documentation. The MATLAB preferences can be set to use Netscape or Internet Explorer as

the browser for help. Two links of interest are Getting Help (at the bottom of the right-hand frame),

and Getting Started which is under MATLAB in the left-hand frame.

(c) Explore the MATLAB help capability available at the command line. Try the following:

help

help plot

help colon %<— a VERY IMPORTANT notation

help ops

help zeros

help ones

lookfor filter %<— keyword search

NOTE: it is possible to force MATLAB to display only one screen-full of information at once by

issuing the command more on).

(d) Run the MATLAB demos: type demo and explore a variety of basic MATLAB commands and plots.

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(e) Use MATLAB as a calculator. Try the following:

pi*pi – 10

sin(pi/4)

ans ˆ 2 %<— “ans” holds the last result

(f) Do variable name assignment in MATLAB. Try the following:

x = sin( pi/5 );

cos( pi/5 ) %<— assigned to what?

y = sqrt( 1 – x*x )

ans

(g) Complex numbers are natural in MATLAB. The basic operations are supported. Try the following:

z = 3 + 4i, w = -3 + 4j

real(z), imag(z)

abs([z,w]) %<– Vector constructor

conj(z+w)

angle(z)

exp( j*pi )

exp(j*[ pi/4, 0, -pi/4 ])

2 Warm-up

2.1 MATLAB Array Indexing

(a) Make sure that you understand the colon notation. In particular, explain in words what the following

MATLAB code will produce

jkl = 0 : 6

jkl = 2 : 4 : 17

jkl = 99 : -1 : 88

ttt = 2 : (1/9) : 4

tpi = pi * [ 0:0.1:2 ];

(b) Extracting and/or inserting numbers in a vector is very easy to do. Consider the following definition

of xx:

xx = [ zeros(1,3), linspace(0,1,5), ones(1,4) ]

xx(4:6)

size(xx)

length(xx)

xx(2:2:length(xx))

Explain the results echoed from the last four lines of the above code.

(c) Observe the result of the following assignments:

yy = xx; yy(4:6) = pi*(1:3)

Now write a statement that will take the vector xx defined in part (b) and replace the even indexed

elements (i.e., xx(2), xx(4), etc) with the constant ππ. Use a vector replacement, not a loop.

Instructor Verification (separate page)

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2.2 MATLAB Script Files

(a) Experiment with vectors in MATLAB. Think of the vector as a set of numbers. Try the following:

xk = cos( pi*(0:11)/4 ) %<—comment: compute cosines

Explain how the different values of cosine are stored in the vector xk. What is xk(1)? Is xk(0)

defined?

NOTES: the semicolon at the end of a statement will suppress the echo to the screen. The text

following the % is a comment; it may be omitted.

(b) (A taste of vectorization) Loops can be written in MATLAB, but they are NOT the most efficient way

to get things done. It’s better to always avoid loops and use the colon notation instead. The following

code has a loop that computes values of the cosine function. (The index of yy() must start at 1.)

Rewrite this computation without using the loop (follow the style in the previous part).

yy = [ ]; %<— initialize the yy vector to be empty

for k=-5:5

yy(k+6) = cos( k*pi/5 )

end

yy

Explain why it is necessary to write yy(k+6). What happens if you use yy(k) instead?

Instructor Verification (separate page)

(c) Plotting is easy in MATLAB for both real and complex numbers. The basic plot command will plot a

vector y versus a vector x. Try the following:

x = [-3 -1 0 1 3 ];

y = x.*x – 3*x;

plot( x, y )

z = x + y*sqrt(-1)

plot( z ) %<—- complex values: plot imag vs. real

Use help arith to learn how the operation xx.*xx works when xx is a vector; compare to

matrix multiply.

When unsure about a command, use help.

(d) Use the built-in MATLAB editor (on Windows-95/98/NT), or an external one such as EMACS on

UNIX/LINUX, to create a script file called mylab1.m containing the following lines:

tt = -1 : 0.01 : 1;

xx = cos( 5*pi*tt );

zz = 1.4*exp(j*pi/2)*exp(j*5*pi*tt);

plot( tt, xx, ’b-’, tt, real(zz), ’r–’ ), grid on

%<— plot a sinusoid

title(’TEST PLOT of a SINUSOID’)

xlabel(’TIME (sec)’)

Note: Do not save this file or any of your MATLAB files to the local hard disk. Your computer

account contains a private networked directory where you can store your own files. Use the MATLAB

command addpath() to allow MATLAB to “see” your personal directory (usually the Z: drive).

Explain why the plot of real(zz) is a sinusoid. What is its phase and amplitude? Make a calculation of the phase from a time-shift measured on the plot.

Instructor Verification (separate page)

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(e) Run your script from MATLAB. To run the file mylab1 that you created previously, try

mylab1

type mylab1

%<—will run the commands in the file

%<—will type out the contents of

% mylab1.m to the screen

3 Laboratory: Manipulating Sinusoids with MATLAB

Now you’re on your own. Include a short summary of this Section with plots in your Lab report.

Write a MATLAB script file to do steps (a) through (d) below. Include a listing of the script file with your

report.

(a) Generate a time vector (tt) to cover a range of t that will exhibit approximately two cycles of the

1250 Hz sinusoids defined in the next part, part (b). Use a definition for tt similar to part 2.2(d). If

we use T to denote the period of the sinusoids, define the starting time of the vector tt to be equal

to −T, and the ending time as +T. Then the two cycles will include t = 0. Finally, make sure that

you have at least 25 samples per period of the sinusoidal wave. In other words, when you use the

colon operator to define the time vector, make the increment small enough to generate 25 samples per

period.

(b) Generate two 1250 Hz sinusoids with arbitrary amplitude and time-shift.

x1(t) = A1 cos(2π(1250)(t − tm1 )) x2(t) = A2 cos(2π(1250)(t − tm2 ))

Select the value of the amplitudes and time-shifts as follows: Let A2 be equal to your age and set

A1 = 1.2A2. For the time-shifts, set tm1 = −(37.2/M)T and tm2 = (41.3/D)T where D and M

are the day and month of your birthday, and T is the period.

Make a plot of both signals over the range of −T ≤ t ≤ T. For your final printed output in part

(d) below, use subplot(3,1,1) and subplot(3,1,2) to make a three-panel subplot that puts

both of these plots in the same figure window. See help subplot.

(c) Create a third sinusoid as the sum: x3(t) = x1(t) + x2(t). In MATLAB this amounts to summing the

vectors that hold the values of each sinusoid. Make a plot of x3(t) over the same range of time as

used in the plots of part (b). Include this as the third panel in the plot by using subplot(3,1,3).

(d) Before printing the three plots, put a title on each subplot, and include your name in one of the titles.

See help title, help print and help orient, especially orient tall.

3.1 Theoretical Calculations

Remember that the phase of a sinusoid can be calculated after measuring the time location of a positive

peak,1 if we know the frequency.

(a) Make measurements of the “time-location of a positive peak” and the amplitude from the plots of

x1(t) and x2(t), and write those values for Ai and tmi directly on the plots. Then calculate (by hand)

the phases of the two signals, x1(t) and x2(t), by converting each time-shift tmi to phase. Write the

calculated phases φi directly on the plots.

Note: when doing computations, express phase angles in radians, not degrees!

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Usually we say time-delay or time-shift instead of the “time location of a positive peak.”

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(b) Measure the amplitude and time-shift of x3(t) directly from the plot and then calculate the phase

(φ3) by hand. Write these values directly on the plot to show how the amplitude and time-shift were

measured, and how the phase was calculated.

(c) Now use the phasor addition theorem. Carry out a phasor addition of complex amplitudes for x1(t)

and x2(t) to determine the complex amplitude for x3(t). Use the complex amplitude for x3(t) to

verify that your previous calculations of A3 and φ3 were correct.

3.2 Complex Amplitude

Write one line of MATLAB code that will generate values of the sinusoid x1(t) above by using the complexamplitude representation:

x1(t) = #e{Xejωt

}

Use constants for X and ω.

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Lab #1

ECES352

2014

INSTRUCTOR VERIFICATION SHEET

Turn this page in to your grading TA.

Name: Date of Lab:

Part 2.1 Vector replacement using the colon operator:

Verified: Date/Time:

Part 2.2(b) Explain why it is necessary to write yy(k+6). What happens if you use yy(k) instead?

Verified: Date/Time:

Part 2.2(d) Explain why the plot of real(zz) is a sinusoid. What is its amplitude and phase? In the space

below, make a calculation of the phase from time-shift.

Verified: Date/Time:

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