CS lecture 2.ppt

8/14/2019 CS lecture 2.ppt

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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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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:

CS lecture 2.ppt

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