Unit2_Systems - EE3210 Signal and Systems Unit 2 Basic...

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EE3210 Signal and Systems Unit 2 Basic Concepts of Systems
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Unit 2: Basic Concepts of Systems 2 Overview of Systems System: any process that results in the transformation of a signal. A system is continuous-time if both input and output are continuous-time. A system is discrete-time if both input and output are discrete-time. x(t) y(t) Continuous-time x[n] y[n] Discrete-time
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Unit 2: Basic Concepts of Systems 3 Example 1: RC Circuit v s ( t ) + v c ( t ) 0 ) 0 ( ) ( 1 ) ( 1 ) ( ) ( ) ( ) ( ) ( ) ( = = + = = c s c c c c s v t v RC t v RC dt t dv dt t dv C t i R t v t v t i Input-Output Relationship Initial Condition
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Unit 2: Basic Concepts of Systems 4 Example 2: Mass-Spring-Damper System Mass M is supported by a spring with stiffness constant K and a damper with damping constant D. An external force x(t) is applied and causes the mass to move with displacement D. M x ( t ) y ( t ) D K ) ( ) ( ) ( ) ( 2 2 t x t Ky dt t dy D dt t y d M = + +
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Unit 2: Basic Concepts of Systems 5 Block Diagram Representation Systems described by linear constant-coefficient differential equations can be represented by a block diagram, showing the interconnections of elementary operations . It is useful because a pictorial representation add to our understanding of the behavior and properties of the system. such a representation is useful for the simulation or implementation of the systems. CT systems: basis for analog computer simulations DT systems: suggestion for implementation in digital hardware
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Unit 2: Basic Concepts of Systems 6 c) Differentiator d) Integrator D a) Adder b) Multiplicator Basic Components (Continuous Time) dt t dx ) ( x ( t ) a x ( t ) a x ( t ) x ( t ) t dt t x ) ( x 2 ( t ) x 1 ( t ) x 1 ( t ) +x 2 ( t ) +
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Unit 2: Basic Concepts of Systems 7 Example Differentiators are difficult to implement and extremely sensitive to errors and noise. ) ( ) ( 1 ) ( ) ( ) ( ) ( t x a b dt t dy a t y t ay t bx dt t dy + = = Example: x ( t ) b / a D y ( t ) -1/ a dt t dy ) ( +
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Unit 2: Basic Concepts of Systems 8 Alternative Representation Rewrite the DE as follows: [] =
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Unit2_Systems - EE3210 Signal and Systems Unit 2 Basic...

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