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Analisis Isyarat dan Sistem

Intan Sari Areni

intan@unhas.ac.id

intan_sariareni@yahoo.com

Materi Kuliah

• Sinyal dan sistem

• Deret Fourier dari sinyal periodik

• Transformasi Fourier waktu kontinu

• Transformasi Fourier waktu diskrit

• Karakteristik waktu dan frekuensi, sampling, sistem komunikasi

• Transformasi Laplace

• Transformasi Z

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Referensi

• Signal & Systems, second edition by Alan V. Oppenheim, publisher Prentice-Hall

• Signal & Systems, Schaum’s Outline by Hwei P. Hsu, Ph.D., publisher The McGraw-Hill Companies, Inc

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Sinyal dan Sistem

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Sinyal / Isyarat

?

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1. Definisi Sinyal

• A signal is a function representing a physical quantity or variable, and typically it contains information about the behavior or nature of the phenomenon

• Signal: any physical quantity that varies with independent variables (time, space, or any other independent variable)

y(t) = 5t2 ; S(x,y) = 3x+4xy+6x2

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N

iiii ttftA

1

))()(2sin()(

Amplitude Frequency Phase

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Example: Signals in an Electrical Circuit

• The signals vc and vs are patterns of variation over time

• Note, we could also have considered the voltage across the resistor or the current as signals

+-

i vcvs

R

C

)(1

)(1)(

)()(

)()()(

tvRC

tvRCdt

tdvdt

tdvCti

R

tvtvti

scc

c

cs

Step (signal) vs at t=1 RC = 1 First order (exponential) response for vc

v s,

v c

t

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Signal

– The Speech Signal

– The ECG Signal

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Signal– The image

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Signal– The image

2. Klasifikasi Sinyal

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ttx cos)(1 tetx )(2

2.1 Continuous-Time versus Discrete-Time Signals:

Continuous-Time or analog signal are defined for every value of time.

are examples of analog signals

x(t)

t0 Analog Signal• Continuous in time. • Amplitude may take on any value in the continuous range of (-∞, ∞).

Analog Processing• Differentiation, Integration, Filtering, Amplification.• Implemented via passive or active electronic circuitry.

2. Klasifikasi Sinyal

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Discrete-Time signals are defined only at certain specific value of time.

• Continuous Amplitude.• Only defined for certain time instances.• Can be obtained from analog signals via sampling.

The function provide an example of a discrete-time signal.

x(n)

n0 1 2 3 4 5 6 7-1

Undefined

Defined

2. Klasifikasi Sinyal

2.2 Analog and Digital Signals:

2. Klasifikasi Sinyal

2.3 Real and Complex Signals:

• A signal x(t) is a real signal if its value is a real number, • A signal x(t) is a complex signal if its value is a complex number.

x ( t ) = x1( t ) + j x2( t )

where x1(t) and x2(t) are real signals and j .

• Deterministic signals: completely specified functions of time. Predictable, no uncertainty, e.g. , with A and are fixed.

• Random signals (stochastic signals): take on random values at any given time instant and characterized by pdf (probability density function). “Not completely predictable”, “with uncertainty”, e.g. x(n) = dice value at the n-th toss.

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)cos()( 0tAtx 0

2. Klasifikasi Sinyal

2.4 Deterministic and Random Signals:

(a) Deterministic signal

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(b) Random signal

3. Basic Signals

Unit Step Function Unit Impulse Function Real Exponential Signals Complex Exponential Signals