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MIT6_003S10_lec07_handout (1)

# MIT6_003S10_lec07_handout (1) - ˙ x t x t X A X index...

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Unformatted text preview: ˙ x ( t ) x ( t ) X A X index shift Delay →R ˙ x ( t ) x ( t ) X A X index shift Delay →R ˙ x ( t ) x ( t ) X A X X 6.003: Signals and Systems Lecture 7 February 25, 2010 6.003: Signals and Systems Relations between CT and DT: Insights from Operators and Transforms February 25, 2010 Concept Map: Continuous-Time Systems Relations among CT representations. Block Diagram System Functional Y Y 2 A 2 + − + − = 1 2 1 X 2 + 3 A + A 2 Mid-term Examination #1 Wednesday, March 3, 7:30-9:30pm. No recitations on the day of the exam. Coverage: Representations of CT and DT Systems Lectures 1–7 Recitations 1–8 Homeworks 1–4 Homework 4 will not collected or graded. Solutions will be posted. Closed book: 1 page of notes ( 8 1 2 × 11 inches; front and back). Designed as 1-hour exam; two hours to complete. Review sessions during open oﬃce hours. Concept Map: Discrete-Time Systems Relations among DT representations. Block Diagram System Functional X + Delay + Delay Y Y 1 = X 1 −R−R 2 Impulse Response Unit-Sample Response h [ n ] : 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 ,... h ( t ) = 2( e − t/ 2 − e − t ) u ( t ) Differential Equation System Function Difference Equation System Function 2¨ y ( t ) + 3 ˙ y ( t ) + y ( t ) = 2 x ( t ) Y ( s ) X ( s ) = 2 2 s 2 + 3 s + 1 y [ n ] = x [ n ] + y [ n − 1] + y [ n − 2] H ( z ) = Y ( z ) X ( z ) = z 2 1 − z − z 2 Concept Map Relations between CT and DT representations. Block Diagram System Functional Differential Equation System Function Impulse Response + 1 + 1 2 X Y − − Y X = 2 A 2 2 + 3 A + A 2 2¨ y ( t ) + 3 ˙ y ( t ) + y ( t ) = 2 x ( t ) Y ( s ) X ( s ) = 2 2 s 2 + 3 s + 1 h ( t ) = 2( e − t/ 2 − e − t ) u ( t ) Block Diagram System Functional Difference Equation System Function Unit-Sample Response + Delay + Delay X Y Y X = 1 1 −R−R 2 y [ n ] = x [ n ] + y [ n − 1] + y [ n − 2] H ( z ) = Y ( z ) X ( z ) = z 2 1 − z − z 2 h [ n ] : 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 ,... C T D T C T D T First-Order CT System Example: leaky tank....
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MIT6_003S10_lec07_handout (1) - ˙ x t x t X A X index...

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