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Continuous Time And Discrete Time Signals

 

A signal is a quantity which contains information. For example, speech, music, the speed of an automobile, etc.

  1. Continuous time signal

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Fig. : Graphical representation of continuous time signal

  1. Discrete time signal

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Fig. : Graphical representation of discrete time signal


Basic Signals

  1. Rectangular pulse: It is given by A = rect(t/2a)

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Fig. : Rectangular Pulse

  1. Unit step function:

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Fig. : Unit Step

  1. Ramp function:

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Fig. : Ramp Pulse

  1. Sampling function: Sa(x) = sinx/X

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Fig. : Sampling Function

  1. Exponential function: Represented by ex

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Fig. : Exponential Function

  1. Unit impulse function/Dirac-Delta function

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Fig. : Unit Impulse Function

  1. Signum function:

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Fig. : Signum Function

Categories of Signals

  1. Energy Signal {x(t) or x(n)}: Its total energy has a non-zero finite value, i.e. 581.png.
    The total energy in continuous time is defined as
    586.png
    In discrete time
    591.png 
  2. Power Signals: The total power has a non-zero finite value. 0 < Px < 
     
    Average power is the average rate at which we utilize energy.
     
    596.png
     
    601.png  

Three classes of signals:

Class 1: Signals with finite total energy, E <  and zero average power, (Energy signal)

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Class 2: 
With finite average power P. If P > 0, then E = . An example is the signal x[n] = 4, it has infinite energy, but has an average power of
P
 = 16 (power signal)

 

Class 3: Signals for which neither P and E are finite. An example of this signal is x(t) = t.

  1. Even and Odd Signal: If signal x(t) = x(-t), then it is an even signal, e.g. Cos x

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Fig. : Even continuous signal
 

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Fig. : Odd continuous signal


If signal x(t) = {–x(–t)}, then it is odd, e.g. sin x shown in fig. 13.

  1. Periodic and Non-periodic Signal : Periodic signals repeats the same pattern for an infinite time as shown in fig. . Expressions for periodic signals :
    622.png
    whereas, a non-periodic signal has a non-repeating pattern. 

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Fig. : Periodic signal

  1. Causal and Non-Causal Signals: If x(t) = 0, for t < 0 & for n < 0, x(n) = 0, then it is a causal signal as shown in fig. 15.

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Fig. : Causal signal





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