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MIT6_003S10_lec06_handout

MIT6_003S10_lec06_handout - 6.003 Signals and Systems...

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index shift Delay → R 6.003: Signals and Systems 6.003: Signals and Systems Z Transform February 23, 2010 Z Transform Z transform is discrete-time analog of Laplace transform. Furthermore, you already know about Z transforms (we just haven’t called them Z transforms) ! Example: Fibonacci system difference equation y [ n ] = x [ n ] + y [ n 1] + y [ n 2] operator expression Y = X + R Y + R 2 Y Y 1 system functional = X 1 − R − R 2 unit-sample response h [ n ]: 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 , 89 , . . . Check Yourself Example: Fibonacci system difference equation y [ n ] = x [ n ] + y [ n 1] + y [ n 2] operator expression Y = X + R Y + R 2 Y Y 1 system functional = X 1 − R − R 2 unit-sample response h [ n ]: 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 , 89 , . . . Y n = h [ n ] R X n What’s the relation between H ( z ) and h [ n ] ? Lecture 6 February 23, 2010 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. Check Yourself Example: Fibonacci system difference equation y [ n ] = x [ n ] + y [ n 1] + y [ n 2] operator expression Y = X + R Y + R 2 Y system functional Y X = 1 1 − R − R 2 unit-sample response h [ n ]: 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 , 89 , . . .
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