Lec. 3: System Basics
EECE233: Signals and Systems
Lecture 3:
System Basics
Prof. Kyung-Tae Kim
Department of Electrical Engineering
POSTECH
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Lec. 3: System Basics
EECE233: Signals and Systems
Contents
• System Basics
• Theme Examples
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Lec. 3: System Basics
EECE233: Signals and Systems
Contents
• System Basics
• Theme Examples
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Lec. 3: System Basics
EECE233: Signals and Systems
System: Interconnection of Operations
• System can be viewed as an interconnection of operations
that transforms an input signal into an output signal with
properties different from those of the input signal
▪ Let the overall operator 𝐻 denote the action of a system
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System: Interconnection of Operations
• Example: Moving average system
▪ Consider a moving average system:
Discrete-time-shift operator:
Communication
with bit errors
for positive k -> from present to past
for negativ k -> from present to futur e
Parallel form
Cascade form
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EECE233: Signals and Systems
Properties of Systems: Stability
• BIBO (Bounded Input, Bounded Output) stability
▪ A system is BIBO stable if and only if every bounded input
results in a bounded output
𝐻
▪ The condition for a discrete-time system can be described in a
similar manner
• Examples
• From an engineering perspective, it is important that a
system of interest remain stable under all possible operating
conditions
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Properties of Systems: Memory
• A system possesses memory if its output signal depends
on past or future values of the input signal
• A system is memoryless if its output signal depends only
on the present value of the input signal
• Examples
memoryless
memory
memoryless
memory
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Properties of Systems: Causality
• A system is causal if the present value of the output signal
depends only on the present or past values of the input
signal
• A system is noncausal if the present value of the output
signal depends on the future values of the input signal
• Examples
causal
noncausal
• The causality is required for a system to be capable of
operating in real time
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EECE233: Signals and Systems
Properties of Systems: Invertibility
• A system is invertible if the input of the system can be
recovered from the output
▪ In other words, there must be a one-to-one mapping
between input and output signals
𝐻
𝐻inv
• In any event, a system is not invertible unless distinct
서로다른
inputs applied to the system produce distinct outputs
• Example
▪ Equalizer – Compensate for the distortion due to the physical
characteristics of the channel in a communication system
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Lec. 3: System Basics
EECE233: Signals and Systems
Properties of Systems: Time Invariance
• A system is time invariant if a time delay or time advance
of the input signal leads to an identical time shift in the
output signal
The system operator 𝐻 and the time-shift operator
𝑆 𝑡0 must commute with each other for all 𝑡0
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Properties of Systems: Linearity
• A system is linear if the system satisfies the superposition
and homogeneity
▪ Superposition:
▪ Homogeneity:
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EECE233: Signals and Systems
Noise
• The term noise is used customarily to designate unwanted
signals that tend to disturb the operation of a system and
over which we have incomplete control
▪ External sources of noise: atmospheric noise, cosmic (galactic)
noise, human-made noise
▪ Internal source of noise (electrical noise): thermal noise, shot
noise, 1/f noise
▪ Electrical noise arises from spontaneous fluctuations of the
current or voltage signal in electrical circuits
• To model noise, a convenient way is to use probability
distribution of the noise, and therefore, the statistical
nature of the noise is determined (random process)
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Noise: Example
• Example: Additive white Gaussian noise (AWGN) in digital
communications
Digital commun. signal
AWGN with variance 𝜎12
Signal with AWGN
Digital commun. signal
AWGN with variance 𝜎22
Signal with AWGN
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Lec. 3: System Basics
EECE233: Signals and Systems
Contents
• System Basics
• Theme Examples
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Lec. 3: System Basics
EECE233: Signals and Systems
Differentiation and Integration - RC Circuits
• Differentiator
If 𝑅𝐶 is small
• Integrator
If 𝑅𝐶 is large
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Radar Range Measurement
• Commonly used signals in radar
▪ Round-trip time of a target at distance 𝑑:
▪ Range resolution: 𝑇0
▪ Range ambiguity:
• Similar range measurement methods are employed with
sound (sonar), ultrasound (biomedical remote sensing),
and infrared (automatic-focusing cameras)
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Moving-Average Systems
• Moving-average systems are often used for the
enhancement of some feature in a dataset
▪ Ex) Identifying the underlying trend in data that are fluctuating
Original data
Output of the MA system
(𝑁 = 8)
▪ General form:
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Multipath Communication Channel
• Multiple propagation paths in a wireless communication
▪ Tapped-delay-line model of a linear communication channel
(assumed to be time invariant)
Sampling
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Multipath Communication Channel
• Major issue: ISI (inter-symbol interference)
• To mitigate an ISI problem, the receiver incorporates an
equalizer, which compensates for dispersion in the
channel
Linear equalizer that
consists of 𝐿𝑓 FIR taps
▪ An ideal equalizer would satisfy
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Multipath Communication Channel
• Example: Considered scenario
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Multipath Communication Channel
• Equalizer with 𝐿𝑓 = 3
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Multipath Communication Channel
• Equalizer with 𝐿𝑓 = 10
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EECE233: Signals and Systems
Recursive Discrete-Time Computation
• First-order recursive discrete-time filter
𝑟 = 1: Accumulator
𝑟 < 1: Leaky accumulator
𝑟 > 1: Amplifier
▪ The term “recursive” signifies the dependence of the output
signal on its own past values
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