Materi 1_Analisis Sinyal.ppt
Transcript of Materi 1_Analisis Sinyal.ppt
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Analisis Isyarat dan Sistem
Intan Sari Areni
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