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Signals & System
Lecture 2
Signals Concepts & Properties
Dr. Tahir Zaidi
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Signals Concepts & Properties
(1) Systems, signals, mathematical models.
Continuous-time and discrete-time signals.
Energy and power signals. Linear systems.
Examples for use throughout the course, introduction
to Matlab and Simulink tools
Specific objectives for this lecture include
• General properties of signals
• Energy and power for continuous & discrete-time
signals
• Signal transformations
• Specific signal types
• Representing signals in Matlab and Simulink
2/25
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Lecture 2: Resources
• SaS, O&W, Sections 1.1-1.4
• SaS, H&vV, Sections 1.4-1.9
• Mastering Matlab 6
• Mastering Simulink 4
3/25
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Reminder: Continuous & Discrete Signals
Continuous-Time Signals
Most signals in the real world are
x(t)
continuous time, as the scale is
infinitesimally fine.
E.g. voltage, velocity,
Denote by x(t), where the time
t
interval may be bounded (finite) or
infinite
Discrete-Time Signals
Some real world and many digital
signals are discrete time, as they
are sampled
x[n]
E.g. pixels, daily stock price (anything
that a digital computer processes)
Denote by x[n], where n is an integer
value that varies discretely
n
Sampled continuous signal
x[n] =x(nk)
4/25
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“Electrical” Signal Energy & Power
It is often useful to characterise signals by measures such
as energy and power
For example, the instantaneous power of a resistor is:
1 2
p(t ) v(t )i(t ) v (t )
R
and the total energy expanded over the interval [t1, t2] is:
t2 t2 1
t1 t1 R (t )dt
2
p (t ) dt v
and the average energy is:
1 t2 1 t2 1 2
t2 t1 t1 p(t )dt
t2 t1 t1 R
v (t )dt
How are these concepts defined for any continuous or
discrete time signal?
5/25
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Distribution of this document is illegal
Signals & System
Lecture 2
Signals Concepts & Properties
Dr. Tahir Zaidi
Downloaded by: atizazahmed |
Distribution of this document is illegal
, Stuvia.com - The Marketplace to Buy and Sell your Study Material
Signals Concepts & Properties
(1) Systems, signals, mathematical models.
Continuous-time and discrete-time signals.
Energy and power signals. Linear systems.
Examples for use throughout the course, introduction
to Matlab and Simulink tools
Specific objectives for this lecture include
• General properties of signals
• Energy and power for continuous & discrete-time
signals
• Signal transformations
• Specific signal types
• Representing signals in Matlab and Simulink
2/25
Downloaded by: atizazahmed |
Distribution of this document is illegal
, Stuvia.com - The Marketplace to Buy and Sell your Study Material
Lecture 2: Resources
• SaS, O&W, Sections 1.1-1.4
• SaS, H&vV, Sections 1.4-1.9
• Mastering Matlab 6
• Mastering Simulink 4
3/25
Downloaded by: atizazahmed |
Distribution of this document is illegal
, Stuvia.com - The Marketplace to Buy and Sell your Study Material
Reminder: Continuous & Discrete Signals
Continuous-Time Signals
Most signals in the real world are
x(t)
continuous time, as the scale is
infinitesimally fine.
E.g. voltage, velocity,
Denote by x(t), where the time
t
interval may be bounded (finite) or
infinite
Discrete-Time Signals
Some real world and many digital
signals are discrete time, as they
are sampled
x[n]
E.g. pixels, daily stock price (anything
that a digital computer processes)
Denote by x[n], where n is an integer
value that varies discretely
n
Sampled continuous signal
x[n] =x(nk)
4/25
Downloaded by: atizazahmed |
Distribution of this document is illegal
, Stuvia.com - The Marketplace to Buy and Sell your Study Material
“Electrical” Signal Energy & Power
It is often useful to characterise signals by measures such
as energy and power
For example, the instantaneous power of a resistor is:
1 2
p(t ) v(t )i(t ) v (t )
R
and the total energy expanded over the interval [t1, t2] is:
t2 t2 1
t1 t1 R (t )dt
2
p (t ) dt v
and the average energy is:
1 t2 1 t2 1 2
t2 t1 t1 p(t )dt
t2 t1 t1 R
v (t )dt
How are these concepts defined for any continuous or
discrete time signal?
5/25
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