eeet2369 lecture 1_presentation

7/30/2019 EEET2369 Lecture 1_Presentation

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EEET2369 Signals and Systems

Introduction to Signals and Systems

Lecturer: Dr Katrina Neville

RMIT University2013 EEET2369 Signals and Systems 2

Lecturer Information

Course coordinator:

Dr Katrina NevilleE-mail: [email protected]: 10.07.09


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Assumed Knowledge

Its recommended that you have successfully completedEEET2248 Engineering Methods (or an equivalent course)before attempting this course.

This course assumes that you have:

The ability to solve basic algebraic equations and sets of linearequations

Competence in basic integral and differential calculus anddifferential equations

Competence in the use of MATLAB for basic programming


Assumed Knowledge

If you have not successfully completed EEET2248 or feel youare weak in these areas, please make use of the studyresources offered by RMIT:

The Study and Learning Centre (SLC) offers maths drop-insessions, advice on report writing and exam preparation.

SLC is located at 12.04.20 (opposite the Hub)Learning Lab (online): http://emedia.rmit.edu.au/learninglab/

Spend some time becoming familiar with MATLAB. A goodbook to get you started is:

W. J. Palm III, Introduction to MATLAB for Engineers, New York: McGraw Hill,2011.


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Course Outcomes

Upon successful completion of this course, you will be able to:

Apply time and frequency domain analysis techniques to differentsignals and systems

Classify signals and systems as discrete/continuous, linear/nonlinear, causal/non-causal, time-variant/invariant, etc.

Select and utilise appropriate methods for basic signal processingapplications

Design basic system simulations in MATLAB


Course Topics

The topics covered in this course include:

Complex exponentials and sinusoids

Time- and frequency-domains of signals

Sampling and reconstruction of signals

FIR and IIR filter design and analysis

Impulse responses, frequency responses and transfer functions ofsystems

Introduction to continuous-time signals and systems


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Course Outline: Assessment

Laboratories (5) (30%)

6% for each laboratory report

Assignments (20%)

Examination (50%)


Laboratory work

Experiment 1: Introduction to MATLAB (Weeks 2 & 3)

Experiment 2: Chirps and Beat notes (Weeks 4 & 5)

Experiment 3: Sampling and reconstruction (Weeks 6 & 7)

Experiment 4: FIR and IIR Filters (Weeks 8 & 9)

Experiment 5: Applications of Filters (Weeks 10 & 11)

Lab experiments are conducted in groups of up to 4 students.


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Laboratory and Tutorial Start Dates

Labs and tutorials start next week (week 2).

Experiment 1: Introduction to MATLAB

Reviews some of the material covered in EEET2248 EngineeringMethods.

Focuses more on the skills needed for Signals and Systems.

Make sure you are correctly timetabled into your lab andtutorial classes before then.

If you havent timetabled into a lab/tute class go to:

http://sts.rmit.edu.au/STS

If you have any problems with timetabling e-mail:

[email protected]


Assignments

There are two assignments this semester each worth 10%.

They will cover the topics

Signals and spectra

Filters

These assignments will be assessed on your ability tocommunicate your comprehension and understanding of theconcepts covered in this course.

To get a HD for these assignments its expected you will beable to clearly explain what is happening and why itshappening.


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Overview of Learning Resources

Course material (i.e. lecture slides, tutorials, lab experiments,etc) are available via myRMIT Studies.

As the lectures are heavily based around the followingprescribed text, it is highly recommended that you purchasethis textbook from the RMIT bookshop.

This book contains a CD with worked solutions and usefulexperimental tasks to help further your knowledge in the area.

J. H. McClellan, R. W. Schafer and M. A. Yoder, SignalProcessing First, New Jersey: Prentice Hall, 2006.


myRMIT Studies

MyRMIT Studies (Blackboard) can be accessed by logging intothe system via the site: http://my.rmit.edu.au and clicking onthe link to Studies.

You will find material related to lectures, labs and tutorials onmyRMIT Studies as well as staff contact details and updates on

important dates.


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Lecture Overview

This lecture will introduce the basic concepts behind signalsand systems.

We will start by considering different types of signals andsystems and see some examples of these.

The second part of the lecture will review sinusoidal signals,how to interpret them and how we can represent these signalsto help with analysis of signals and systems.


Introduction to Signals and Systems

The main aim of this course is to introduce the basic conceptsbehind signal processing.

Signal processing is a vast area and has many applications inthe Electronic and Communication Engineering disciplines.

Signal processing can be broken down into two main areas;digital signal processing and analogue signal processing.

This course will consider:

How we can obtain different types of signals

How are signals mathematically represented

What sorts of manipulations can we do to these signals, and

What systems can we design and utilise to process thesesignals


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RMIT University2013 EEET2369 Signals and Systems

What are signals?

Write down what you think a signal is.

Write down some examples of signals that you can think of.

Discuss with people around you if youd like.


Analogue (Continuous) Signals

There are three main types of signals that we will look at thissemester; analogue, discrete and digital.

Most signals are originally in the form of analogue signals,they are continuous in both time and amplitude.

Examples of continuous time/amplitude signals are: voice,music and video.


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Discrete-Time Signals

Discrete-time signals are often obtained by sampling ananalogue signal at set time instances.

Discrete-time signals are still continuous in amplitude but noware only defined at certain time instants.

These types of signals are used in some communicationsystems where multiple signals are transmitted during differentclock periods.


Digital Signals

Digital signals are discrete inboth time and amplitude andare represented assequences of 1s and 0s.

They are obtained by

sampling an analogue signal(making it discrete in time),quantising (making itdiscrete in amplitude) andencoding (assigning a binaryvalue to the samples).

Digital audio, video andimages are examples ofdigital signals.


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What are Systems?

Write down what you think a system is.

Write down some examples of systems that you can think of.

Discuss with people around you if youd like.


Analogue Systems

Analogue systems are designed to process continuous(analogue) signals.

Apart from mechanical systems, analogue systems have beenaround the longest.

In Circuit Theory in first year we looked at simple analoguesystems made up of devices such as diodes, resistors,capacitors, inductors, etc.

A simple, passive low-pass filter (RLC configuration)


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Digital Systems

Digital systems have become very popular since the 1970swhen digital computing started to become more common.

Digital systems process ones and zeros that have often beengenerated from sampling and quantising an analogue signal.

Microprocessors are common systems used in digital signalprocessing, these devices are often programmed to performappropriate operations on a digital signal.

Image from Texas Instruments website: http://www.ti.com/tool/tmdxevm6670


Mathematical Representation of Signals and Systems

Some common terms to mathematically represent signals andsystems are given:

: for analogue signals and systems the bracketed (t) isconventionally used to represent continuous-time.

: the square bracketed [n]is also a convention used to

represent discrete-time and will be commonly seen whenconsidering discrete-time signals and systems.

is another term used to say that an output signalis obtained by passing the input signal, though some systemwith a time-domain response, (see figure).

)(tx

][nx

)}({)( txTty = )(ty

{}T

)(tx

Output

)( ty

Input

)(txSystem,

{ })()( txTty =

{}T


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Review of Sinusoids

Sinusoidal signals are one of the simplest types of signals toanalyse.

The next part of this lecture will recap sinusoidal signals andlook at some of the useful identities to help in examining them.


Sinusoidal Signals

The general formula for a co-sinusoidal waveform is given as:

Similarly for a sinusoid the general formula is given as:

For both these signals represents the amplitude of thewaveforms, i.e. the waveform will oscillate between .

is the radian frequency. Radian frequency is found fromthe frequency in Hertz by multiplying by .Therefore: .

Finally is the phase shift of the waveform, or where in thecycle the waveform will begin. In signal processing this is alsorepresented in radians.

0

)cos()( 0 += tAtx

A

)sin()( 0 += tAtx

2rad/sec2 00 f=

Hz0f

A


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Trigonometric Identities

The following trigonometric identities are often used to simplifymathematical representations of sine and cosine signals to aidin analysis.

1.

2.

3.

4.

5.

6.

7.

)(sin)(cos)2cos( 22 =

1)(cos)(sin 22 =+

)cos()sin(2)2sin( =

)sin()cos()cos()sin()sin( bababa =

)sin()sin()cos()cos()cos( bababa m=

( ))2cos(12

1)(cos2 +=

( ))2cos(12

1)(sin2 =


Example 2-1: Plotting Sinusoids

Plot the function:

What is the amplitude?

What is the frequency?

A single period of this waveform is?

And what is its phase-shift? (in radians and degrees):

]4.0)40(2cos[20)( = ttx


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So far.

So far we have looked at the classification of signals andsystems and seen some examples of these.

Weve also reviewed sinusoidal signals and the parametersthat define the phase, frequency and amplitudes of sinusoids.

In the next part of this lecture we will look at some of themanipulations that can be performed on signals, how tomathematically represent these and how these manipulationscan be recognised from the signals mathematical form.


Manipulation of Signals

Its good to be able to identify certain manipulations to a basesignal function by observing changes to its mathematical form.

Changes to a signal can easily be identified by observing themathematical function that defines a signal.

Changes to time-delay/phase, amplitude, frequency (in periodicfunctions) or dilation/contraction can easily be identified fromobservations about the function.


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Time-Shifting Signals

In the sinusoid example we saw a phase-shift of a sine wavewill give some sort of time-shift in either the positive or negativetime direction.

There are some basic rules for time-shifting that apply to allsignals and will be used a great deal this semester.

Lets consider a simple square pulse:

=elsewhere,0

2t0,1)(tx


Time-Shifting Signals

What will look like? )3( +tx)2( tx What will look like?


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Time-Shifting Signals (cont)

What will look like? )3( +tx)2( tx What will look like?

=elsewhere,0

4t2,1)2(tx

=+elsewhere,0

1t3-,1)3(tx

What general rule can we apply here?


Relating Phase-Shift (in Periodic Functions) to Time-Shift

For the previous sinusoid example:we can use the rules for time-shifting a signal to say this is thesame as: .

i.e.

In general, to relate phase-shift to time-shift we can use:

]4.0)40(2cos[20)( = ttx

)]005.0)(40.2cos[(20)( = ttx

A time-shift of 0.005 secin the +ve direction

originalassame]4.0)40(2cos[20)(

)]2.0(2)40(2cos[20)(

)]005.0(402402cos[20)(

)]005.0)(40.2cos[(20)(

=

=

=

=

ttx

ttx

ttx

ttx

02 fT

=


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Time-Flipping Signals

What will look like? What will look like?)3( tx )( tx


What will look like?

Time-Flipping Signals (cont)

What will look like? )3( tx )( tx

=elsewhere,0

3t1,1)3( tx

=elsewhere,0

0t2-,1)( tx



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Time-Scaling of Signals

What will look like? And finally ?( )2/tx)3( tx


What will look like?

Time-Scaling of Signals (cont)

What will look like? ( )2/tx)3( tx

=elsewhere,0

4t0,1)2/(tx


=elsewhere,0

667.0t0,1)3( tx


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Time-Scaling of Signals (cont)

Discuss if this rule would still apply for periodic functions.

What would you predict will occur when applying this toperiodic functions?

Write down your predictions. Speak to people near you if youdlike.


Other Common Signals (Briefly)

Unit step function (a.k.a. Heaviside step function): thisfunction is often used to help define signals that begin at acertain time and stay on for an infinite duration after thatspecified time.

eeet2369 lecture 1_presentation

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