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Introduction to Signals
Chapter 2
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IntroductionSignals can be seen as inputs/outputs to systems
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Signal energy and power
Quantifying the size of a signal is important in many applications
How much electricity can be used in a defibrillator?
How much energy should an audio signal have to be heard?
Some signals have infinite energy. In that case, we may use the
concept of average signal power
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Size of a SignalSize of Signal
Size of any entity is the number that indicates the largeness or strength of that entity Generally the amplitude varies with time.
Signal amplitude and duration gives better information about the size
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Signal Power
Fig. 2.1:
a. Signal with finite Energy
b. Signal with finite power
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Units of Energy and Power
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Solution
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Solution
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Classification of Signals
Continuous time and Discrete time signals
Analog and Digital Signals
Periodic and Aperiodic Signals
Energy and Power Signals
Deterministic and Probabilistic Signals
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Continuous time and Discrete time signals
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Analog and Digital Signals
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Periodic and Aperiodic Signals
We only need define the signal over one period and we know everything about it
Sinusoids and constant are clearly periodic signals. Other examples include
periodic pulses (rectangular and triangular pulses)
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Energy and Power Signals
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Deterministic and Probabilistic Signals
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Some Useful Operation
Time Shifting
Time Scaling
Time Inversion (Time Reversal)
Unit Impulse Function
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Time Shifting
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Time Scaling
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Time Scaling..
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Time Inversion (Time Reversal)
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Unit Impulse Function
The impulse function is not a function in the ordinary sense because its value at zero is not a real
value. It is represented by a vertical arrow. The impulse function is unbounded and discontinuous
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Multiplication of a Function by an Impulse
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Sampling Property of the Unit Impulse Function
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Unit Impulse Function as a Generalized Function
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The product signal g(t)u(t) for any g(t) can be thought of as the signal g(t) turned on at time t = 0.
Used to check how a system responds to a sudden input
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2.45
Discussion
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Discussion
The term "autocorrelation" is the name of the operation when a function is correlated with itself.
The autocorrelation is denoted when both of the subscripts to the Correlation operator are the same: