Lab 1 Finished!

8/18/2019 Lab 1 Finished!

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Abstract

Based on the title, Discrete and Continuous time Signal and Convolution, we will be

introduced to the Matlab commands to create a discrete and sinusoidal waveform by a specific

function and variety data. Then, we will be taught to convolute two functions.

Objective

The purpose of this task is to illustrate the properties of continuous and discretetime

signals using Matlab software environment.

Project background

Continuous time signal is a signal that will contain a value for all real number along the

time a!is. "n contrast for discrete time signal which created by sampling a continuous signal.

Means that only have values at specific time with an e#ually interval for each times.

Convolution is a mathematical operation on two functions that will produce a third

function that has been modified by combination of those two earlier functions.

Procedures

Task 1

Two set of command was typed in the Matlab software. The output waveform was observed and

analy$e.

a% &isting '


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b% &isting (

Task 2

) set of command was written in the Matlab command window with a sampling fre#uency,

fundamental fre#uency and amplitude was given.


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The same command was written on the Matlab command window but the value of amplitude,

fundamental fre#uency and sampling fre#uency was changed twice.

*irst

Second


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Task 3

) command was written for given function with a specified intervals. The waveform of the

function was observed and analy$e.

a% sinc+t% in '-pi, '-pi / rect+t% in (, (

Then, a command to create a discretetime function was written with function of a^n(u(n))-u(n-

10)) in -20, 20]


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Task

) command to obtain a discrete time convolution waveform was written. The waveform was

observed and analy$e.


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!esu"t and #iscussion

Task 1

0 10 20 30 40-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

$oding

n0-1(12-3 4describing array

y0sin+n/2%3 4declaration of variable to sin function

subplot+5,','%3 4located the output

stem+n,y%3 4display discrete data

%uestion 1

Explain the effect of each command in Listing 1. You may need to draw, sketch or print out

any figures graphs in your explanation?

*or the first command, it was describing a group of arrayfrom - to 2- with an increment

of (. The ne!t line commanded the declaration of a variable e#ual to sin function. Third

command will located the output waveform by respecting to the matri! command. &ast

command is about to display discrete se#uence data.


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%uestion 2

From your obseration, is listing 1 generating a continuous!time or discrete!time signal?

Discretetime signal data data will be generate because the data use command of 6stem7.

%uestion 3 (coding)

n'0-1(12-3 4"For the first command, it is describing a group of array from # to $# with an

increment of %&

$0sin+n'/2%3 4"second line command is about declaration of sin function which an array that

has been set up before as ariable of the function&

subplot+5,','%3 4"by respecting to the matrix command , it will located the output waeform&

plot+n',$%3 4"show that connection of plot point to be able display signal which looks like a

continuos time signal&

n(0-1'-12-3 4"'t is describing a group of array from # to $# with an increment of %&

w0sin+n(/2%3 4"'s about declaration of sin function which an array that has been set up

before as ariable of the function&

subplot+5,',5%3 8 4"by respecting to the matrix command , it will located the output waeform&

plot+n(,w%3 4"show that connection of plot point to be able display signal which looks like a

continuos time signal&

%uestion

(lot the graph obtained from the command aboe?

0 10 20 30 40-1

-0.5

0

0.5

1

0 10 20 30 40-1

-0.5

0

0.5

1


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Task 2

%uestion &

(lot the graph obtained from the commands in Listing )?

0 0.5 1 1.5 2 2.5 3 . .

-1

-0.5

0

0.5

1plot of a cosine waveform

A m p l i t u d e

time

0 5 10 15 20 25-1

-0.5

0

0.5


A m

p l i t u d e

samples

$oding and e'"anation

Clc3

clf3

90583 4"declaration of ariable with its own alue&)0'3 4"declaration of ariable with its own alue&

fl0'---3 4"declaration of ariable with its own alue&fs0:---3 4"declaration of ariable with its own alue&

ts0'/fs3 4"declaration of ariable with mathematical operation& t0-1ts19;ts3 4"describing a group of array with beginning, increment and ending alue&

!0);cos+(;pi;fl;t%3 4+declaration of ariable with cos function&

figure+'%3subplot+(,','%3plot+t,!%3 4"located and plot the waeform&title+


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%uestion

+rite a program in -L-/ with different fundamental fre0uency and sampling fre0uency?

a%

0 0.5 1 1.5 2 2.5 3 . .

-1.5

-1

-0.5

0

0.5

1

1.5plot of a cosine waveform

A m p l i t u d e

time

0 5 10 15 20 25-1.5

-1

-0.5

0

0.5

1

1.5plot of a cosine waveform

A m p l i t u d e

samples


clc3

clf3 90583 4"declaration of ariable with its own alue&

)0'.83 4"declaration of ariable with its own alue&

fl0'8--3 4"declaration of ariable with its own alue&fs0:---3 4"declaration of ariable with its own alue&ts0'/fs3 4"declaration of ariable with mathematical operation&

t0-1ts19;ts3 4"describing a group of array with beginning, increment and ending alue&!0);cos+(;pi;fl;t%3 4+declaration of ariable with cos function&figure+'%3subplot+(,','%3plot+t,!%3 4"located and plot the waeform&

title+


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b%

0 0.5 1 1.5 2 2.5 3 . .

-2

-1

0

1


A m p

l i t u d e

time

0 5 10 15 20 25-2

-1

0

1


A m p l i t u d e

samples


clc3

clf3 90583 4"declaration of ariable with its own alue&

)0(3 4"declaration of ariable with its own alue&

fl0(---3 4"declaration of ariable with its own alue&fs0:---3 4"declaration of ariable with its own alue&ts0'/fs3 4"declaration of ariable with mathematical operation&

t0-1ts19;ts3 4"describing a group of array with beginning, increment and ending alue&!0);cos+(;pi;fl;t%3 4+declaration of ariable with cos function&figure+'%3subplot+(,','%3plot+t,!%3 4"located and plot the waeform&

title+


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Task 3

%uestion *

+rite the commands you used in soling the problem pecial Function?

+)%

-40 -30 -20 -10 0 10-0.5

0

0.5

1

-2 -1.5 -1 -0.5 0 0.5 .0

0.5

1

t0'-;pi1-.'1'-;pi3 4"describing a group of first array from !1#pi to 1#pi with an increment#f #.1&

s0(1-.'1(3 4"describing a group of second array from !% to % with an increment #f #.1&

y0sinc+t%3 4"declaration of ariable respect with a sinc function&$0+abs+s%=0-.8%3 *"declaration of ariable by computing that mathematical function&

subplot+5,',(%3plot+t,y%3 *"located and plot the waeform&subplot+5,',5%3plot+s,$%3 *"located and plot the waeform&


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+B%

-20 -15 -10 -5 0 50

0.2

0.4

0.6

0.8

-20 -15 -10 -5 0 50

0.5

1

-20 -15 -10 -5 0 50

20

40

60

u0inline+-


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+C%


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Task

0 5 10 150

0.5

1

1.5

2

x ( n T )

0 5 10 150

0.5

1

1.5

2

h ( n T )

$oding

!0- ' ' ' ' ' ' ' ' ' ' ' ' '3h0' -.8 -.(8 -.'(8 -.-2(83

y0conv+!,h%3

n$0'-3ly0length+y%@n$3

!$0!,$eros+',lylength+!%%3

h$0h, $eros+',lylength+h%%3

y$0y, $eros+',n$%3nn0-1ly'3

subplot+5,','%,stem+nn,!$,

!label+


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and continuous signal. Besides, we achieve to obtain a discrete time convolution

using Matlab and manually.

Lab 1 Finished!

Documents

Transcript of Lab 1 Finished!