Lect Chapter1 Part1

8/4/2019 Lect Chapter1 Part1

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Introduction:Fundamental Concepts

Br. Khaizuran Abdullah

Department of Electrical and

Computer Engineering

International Islamic University Malaysia

ECE 2221 : Signals and Systems (Analysis) Sem. II (04/05)

Lecture Chapter 1 (Part 1)


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Questions?

Whats signal?

Whats system?


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Introduction:Signals and Systems: What are they?

A time-varying physical phenomenon to convey

information/message

Signal:

a dogs barking, traffic lights, a cars signal, emergency

light, a red light on top of a building, a heartbeat of a

patient, a blood pressure of a patient

Examples:


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Introduction:Signals and Systems: What are they?

System:

a combination of several components to

perform a desired task. It processes

input signal to produce output signal

a communication system, a human sense system,

a traffic controller. Refer to CommSys.doc

Examples:
http://commsys.doc/http://commsys.doc/


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Classification of signals

CT or DT

Deterministic Random/stochastic

Periodic Aperiodic

Complex Transient Almostperiodic

Sinusoid

Power, Energy

Even or Odd


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CT and DT Signals

Examples of CT and DT are shown in these figures

A signal x(t) is said to be a continuous-time signal if it is defined for all time t.Example of a continuous signal? A sine wave signal

Example of a NOT continuous signal? A unit pulse signal

Is defined only at discrete instant of time

Is obtained by sampling the CT signal at a uniform rate

sampling means that acquiring the values of a signal at discrete pointsin time and not between them.

Is a function of an argument that takes values from a discrete set

~x[n] wheren {...-3,-2,-1,0,1,2,3...}~We sometimes use index instead of time when discussing

discrete-time signals~Values forx may be real or complex

Continuous-time signal:

Discrete-time signal:
http://ct_dt.doc/http://ct_dt.doc/


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Deterministic and Random Signals

Deterministic signal:

Signal which can be completely modeled as function of

time.

Random signal:

Signal which is processed using probability theory.

Examples: x1(t) = sin(20t) for all tx2(t) = cos(20t) for all t

Examples ofdeterministic and random signals
http://det_random.doc/http://det_random.doc/


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Periodic and Aperiodic Signals

Periodic signal has the property that x(t)=x(t+T) for all t.

The smallest value ofT that satisfies the definition is called

the fundamental period.

Below is an example of a periodic signal with T = 0.2 s :

Periodic Signal?


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Periodic and Aperiodic Signals

Aperiodic Signal?

Any signal x(t) for which no value of T satisfies the

condition of x(t) = x(t+T)

Below is an example of aperiodic signal:


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How to prove Periodic or Aperiodic

To prove periodic, we need to determine T first:

For a simple sinusoid signal such as x(t)=10 sin(12t), T= 1/6 (rational

number)

Then use x(t + 1/6) = x(t) to confirm that its periodic:

txandwheret

ttt

ttx

02sin12cos12sin10

12cos2sin2cos12sin10212sin10

6

112sin10

6

1


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How to prove Periodic or Aperiodic

For a sum or a product of 2 signals, such as the following examples, it is periodicif the ratio of their respective periods can be expressed as a rational number.

Try these:

1. x(t)=10 sin(12t) + 4 cos (18t)

=> periodic, T1 =1/6 (rational) T2 =1/9 (rational) , T = 1/32. x(t)=10 sin(12t) + 4 cos (18t)

=> aperiodic, T1 =1/6 (rational) T2 = /9 (irrational), T = undetermined

3. x(t)=10 cos(t) + sin (4t)

=> periodic, T1 = 2 (rational) T2 = 1/2 (rational), T = 2

Then, for those which are periodic, use x(t + T) = x(t) to confirm that they areperiodic. (try confirming them !)


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Even and Odd Signals

Even Signal:

x(t) is an even signal if it is satisfies

For example,

tfortxtx

txtxThus

ttttx

ttx

,

2cos2cos2cos

2cos


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Even and Odd Signals

Odd Signal:

x(t) is an odd signal if it is satisfies

For example,

tfortxtx

txtxThus

ttttx

ttx

,

2sin2sin2sin

2sin


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Energy and Power Signals

dttxE

2

2

2

21lim

T

TT

avedttx

TP

T

Tt

t

avedttx

Tdttx

TP

22 110

0

For periodic signal :

If x(t) is a CT signal, its signal energy is

However, this energy integral will not converge if it is infinite. An example of a

CT signal with infinite energy would be the sinusoidal signal

In this case, it is convenient to deal with the average signal power of the signalinstead of the signal energy. The average signal power of a CT signal is

tAtx0

cos


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Energy and Power Signals

Examples:

A) Find the total energy of the rectangular pulse shown in the figure below.

x(t)

t

T

A

B) Find the average power of the square wave shown in the figure below.

x(t)

0.2 0.4-0.2 0

B

-B

Answer: A2T

Answer: B2


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Thank You

Lect Chapter1 Part1

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