lab1

Signals and

Systems Lab 1 Lab instructor : Maheen Islam

Contact: [email protected]

Signals And Systems Lab - Lab engineer Maheen Islam- Electrical Department-Air University 1

Announcements

CR

Class group-mail

Manuals to be submitted in each lab and to be collected from office by CR before Friday every week.

Lab manual to be followed

Marks division

Quizzes 6%

Project 6%

Lab Notebook 3%

Assignments 3%

Lab performance 2%

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Introduction

Lab manual (individual)

Matlab Excercises practiced in lab

Submission in every Lab, Cr to collect manuals every Friday

from office.

Quiz (Unannounced Anytime in Lab)

Assignments (done in manual)

Project Submission

Attendance within First 10 minutes

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Objective of the Lab

Signals and systems analysis - a fundamental course

with various topics having applications in many areas

of engineering such as

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Signals and System

Digital signal

processing

Communication

systems

Control engineering

Image Processing

Radar Engineering

System-Design

4

Announcement Regarding Projects

Project Proposal deadline: Week

before mids.

Failure of submission till

deadline will result

in deduction of 2%

marks and a project

will be assigned.

Flow of the Lab

Introduction of Matlab

Introduction of signals

Difference of continuous time and discrete time signals, system properties

Topics under focus

Convolution, Fourier series, Continuous time Fourier transform (CTFT), discrete time Fourier transform (DTFT), Z- transform.

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Signals and Systems Labs

Lab 1 GETTING STARTED WITH MATLAB

Lab 2 LOOPS & DECISION MAKING

Lab 3 WORKING WITH FUNCTIONS IN MATLAB

Lab 4 HOW TO PLOT DIFFERENT FUNCTIONS IN MATLAB

Lab 5 TRANSFORMATION OF SIGNALS IN MATLAB

Lab 6 CONVOLUTION OF LTI SYSTEMS IN MATLAB

Lab 7 FOURIER SERIES REPRESENTATION OF PERIODIC SIGNALS IN MATLAB

Lab 8 FOURIER TRANSFORM OF DIFFERENT SIGNALS IN MATLAB

Lab 9 Z-TRANSFORM & INVERSE Z-TRANSFORM

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GETTING STARTED WITH

MATLAB

Lab 1

Signals And Systems Lab - Lab engineer Maheen Islam-Electrical Department-Air

University 7

Introduction

Product by MathWorks

Supported Platforms-Windows, MAC and LINUX

Strong Online Help by MathWorks

http://www.mathworks.com

Versatile Tool

Contains a large collection of built- in functions and commands used in

an interactive mode, when you are in the command window

Special Packages for disciplines like control systems, digital signal

processing, communications engineering, and image processing.

More than 20 sets known as toolboxes


University

8

Numerical

Computation

Data

Analysis

Graphical

Visualization

Software

and

Hardware

interface

Matlab GUI


University 9

Command

Window

Matlab

Workspace

Current

Folder

Editor

Window Simulink

Figure Window- all figures and plots generated by plot commands

appear in this window

Commands

THE SAVE COMMAND: If you want to save the variables in the workspace before you quit, use the command SAVE. This automatically

saves all the variables in a file called matlab.mat. When you enter

MATLAB again, you can restore these variables with the command

LOAD.

clc COMMAND: It clears the command window during a work session.

Clear COMMAND: It deletes all the variables in the workspace. All

variables are cleared & cannot be retrieved.

Help COMMAND: simplest way to determine the syntax & behaviour of

a particular function.

Try help whos


University 10

Notes

Data type LESS language, caters everything in the form matrices

MATLAB is case sensitive i.e; time, Time, TIME are three different variables.

To recall previous commands MATLAB uses the up & down arrow keys.

Keys are used to edit the commands.

All text after percent sign (%) is taken as a comment statement.

Multiple commands can be placed on one line if they are separated by commas (,) or semicolons (;).Commas tell MATLAB to display results, semicolons suppress printing.

Ctrl+R => comment, ctrl+T=> uncomment

If a statement does not fit on one line use three periods,, followed by Enter to indicate that the statement continues on the next line. The maximum number of characters allowed on a single line is 4096.

You can interrupt MATLAB execution at any time by pressing CTRL+C.


University 11

Vector, Array and Matrices

Notation used by Matlab is the standard linear algebra notation

Vectors and scalars- special cases of a matrixall of which are represented as arrays in MATLAB

A scalar is an array of 1 1 dimension

A row vector is an array of 1 n dimension

A column vector is an array of n 1 dimension.

When elements of an array are typed in a row within square brackets,

with a space between the elements, MATLAB displays it as a row vector


University 12

Vector, Array and Matrices

Try it

A = [1 2 0 3 1 5] % A row vector with name A

[1 2 0 3 1 5] % will create a row vector with default name ans

B=[1 2 0; 3 1 5; 0 4 -2] % will display a 3x3 matrix, each ; shows next row

>> x = 5 % Real scalar

>> x = 5+10j (or >> x = 5+10i) % Complex scalar

>> x = [1; 2; 3] % Column vector

Note

Complex elements of a matrix should not be typed with spaces, i.e.,

-1+2j is ne as a matrix element, -1 + 2j is not. Also, -1+2j is interpreted correctly whereas -1+j2 is not (MATLAB interprets the j2 as the name of a variable. You can always write -1+j*2


University 13

Matrix Operations-Arithmetic Operators Some more operations and their syntax

Addition +

Subtraction -

Multiplication *

Power or exponent ^

Transpose e.g A

Left division \

Note: x=M\b gives solution to M*x=b solution is given by x = 1 b

Right division /

Note: x=M/b gives solution to x*M=b given by x=M* 1

x = 5;

F=x*C ;

FF=C/x; % will give error at x/C as matrix dimension wont be matching,

to cater this error use dot operator will be discussed later.


University 14

Matrix Operations-Relational Operators

< less than

greater than

>= greater than or equal to

== equal to

~= not equal to

THE LOGICAL OPERATORS, e.g., & (and), | (or), and ~

(not).


University 15

Matrix Operations Dot Operator:use a dot before the sign for the mathematical

operation between the two matrices. e.g (.*), (./), (.^)

Concatenation: A matrix can be expanded by adding new matrices

and column or row vectors

Colon Operator: : J:k IS THE SAME AS [ J, J+1 K] and J:K IS EMPTY IF J>K

Try It:

A=[1 2 1;0 1 1;2 1 1];

B=[2 1 0;1 1 1;-1 2 1];

F=[A B] % horizontal concatenate

b=[5 4 2];

G=[A;B;b]; % vertical concatenate

G(7,2) %access element in 7th row, 2nd column

G(7,2)=6 % change its value to 6


University 16

Matrix Operation

Colon Operator:

Can be used to extract a sub matrix from a matrix

Q(:,2) gives a sub matrix with elements in all rows and the second column only.

The command Q(3,:) gives the elements in all columns and the third row only.

The command Q(1:2,2:3) gives the elements in the rows from 1 to 2 and in the columns from 2 to 3

Q(:,:)

rot90(A) Rotates the matrix array by 90?

fliplr(A) Flips the columns left to right

flipud(A) Flips the rows up to down

triu(A) Gives the upper triangular part of the matrix

tril(A) Gives the lower triangular part of the matrix


University 17

it will return the whole matrix.

Few Special Matrices and Variables

ones(m,n), which gives a matrix with the number one in all its m rows and n columns

zeros(m,n), which gives a matrix with zeros in all its m rows and n columns

eye(m), which gives the identity ma trix of order m m.

Ans the default variable used for the most recent result. And this variable is also used as a default variable to store any value.

Pi it has the value of 3.14

Eps the smallest number such that when added to 1 creates a number greater than 1

Inf stands for infinity (8 1/0)

I or j i=j=v-1


University 18

Special Operations with

Complex Numbers

>> x = 3+4j % Complex scalar

x >> real(x) = 3 % Real part

x >> imag(x) = 4 % Imaginary part

x >> abs(x) = 5 % Magnitude

x >> angle(x) = 0.9273 % Angle

x >> conj(x) = 3 - 4i % Complex conjugate


University 19

Pre-defined functions


University 20

Try your self using Matlab Help. Included in course

Notes

When we use the same variables used above but define

them with new values, they become the current values

for the variables

Solve Exercise 1.91 from manual


University 21

Exercise-1.91

1. Create a vector

a) A of even whole numbers between 31 and 75.

b) B of odd whole numbers between 74 and 131.

2. Let x=[2 5 1 6];

a) Add 16 to each element.

b) Add 3 to the odd indexed element.

c) Compute the square root of each element.

d) Compute the square of each element.

3. Let x = [3 2 6 8] and y = [4 1 3 5]

a) Add the sum of the elements of x to y

b) Raise each element of x to the power specified by the corresponding element of y.

c) Multiply each element in x by the corresponding element in y and store the result in z.

d) Evaluate x*y and interpret the result


University 22

Exercise-1.91

4. given a vector t = [1:0.2:2] write down the MATLAB

expressions that will correctly compute the following

a) ln(2 + t + t2 )

b) ( 1+ cos(3t) )

c) cos2(t) + sin2(t)

d) tan-1 (1)

e) 1+2t


University 23

Practice Lab Task

Create a matrix of dimensions 4x4.

Find the number of diagonal entries and Add even

number to each diagonal locations of the matrix.

That is:

A =

1 2 3 4

4 5 6 6

7 8 9 0

1 2 4 0


University 24

A =

1 2 3 4

4 7 6 6

7 8 13 0

1 2 4 6

lab1

Documents

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lab instructor

lab performance

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