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LINEAR SEQUENTIAL MACHINE AND REDUCTION OF LINEAR SEQUENTIAL MACHINE

LINEAR SEQUENTIAL MACHINE AND REDUCTION OF LINEAR SEQUENTIAL MACHINE. (I) Time Domain (2) Frequency Domain. Module 2 Operation (0 and 1). and so on…. Note: A is always square matrix and gives number of delays Number of columns in B gives number of inputs

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LINEAR SEQUENTIAL MACHINE AND REDUCTION OF LINEAR SEQUENTIAL MACHINE

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  1. LINEAR SEQUENTIAL MACHINE AND REDUCTION OF LINEAR SEQUENTIAL MACHINE Linear Sequential Machines

  2. (I) Time Domain (2) Frequency Domain Linear Sequential Machines

  3. Linear Sequential Machines

  4. Linear Sequential Machines

  5. Linear Sequential Machines

  6. Linear Sequential Machines

  7. Linear Sequential Machines

  8. Module 2 Operation (0 and 1) and so on….. Linear Sequential Machines

  9. Note: • A is always square matrix and gives number • of delays • Number of columns in B gives number • of inputs • Number of rows in C gives number of • output • Order of A and C should be compatible • with present state and order of B and D • should be compatible with input Linear Sequential Machines

  10. Example 1: Linear Sequential Machines

  11. State Space Representation: Linear Sequential Machines

  12. Note: Y’s represent Next State y’s represent Present State z’s represent Output State Here, we have 3 delays, one input and two outputs Linear Sequential Machines

  13. Linear Sequential Machines

  14. Representation: Linear Sequential Machines

  15. Example 2: Determine Characterizing matrices A,B,C and D from the given linear circuit diagram Hint: From fig.,A=2 X 2,B=2 X 1,C=1 X 2 Linear Sequential Machines

  16. From the figure, Y1 = y2 + x Y2 = y1 + x z = y1 + x Linear Sequential Machines

  17. Solution: Linear Sequential Machines

  18. Reduction of Linear Sequential Machines Reduction of linear sequential machines means reducing or minimizing the number of delays Linear Sequential Machines

  19. Example 3: Minimize (reduce) the linear machine given by following characterizing matrices A,B,C,D (Example Kohavi Page-580) Linear Sequential Machines

  20. Reduction: The rank of the diagnostic matrix is 3, and hence the dimenstion of given linear machine CANNOT be reduced Linear Sequential Machines

  21. Example 3: Minimize the linear machine given by following characterizing matrices A,B,C,D (Example Kohavi Page-582) Linear Sequential Machines

  22. Linear Sequential Machines

  23. Linear Sequential Machines

  24. Linear Sequential Machines

  25. Linear Sequential Machines

  26. A* = TAR B* = TB C* = CR D* = D Linear Sequential Machines

  27. Note: In reduction number of Inputs and Outputs do not change and only the number of delays change Linear Sequential Machines

  28. Example 4: Minimize the linear machine given by following characterizing matrices A,B,C,D (Example Kohavi Page-584) Linear Sequential Machines

  29. Linear Sequential Machines

  30. Linear Sequential Machines

  31. Linear Sequential Machines

  32. Linear Sequential Machines

  33. Linear Sequential Machines

  34. A* = TAR B* = TB C* = CR D* = D Linear Sequential Machines

  35. Example 5: Minimize the linear machine given by following characterizing matrices A,B,C,D (Example Kohavi 15 - 19) Linear Sequential Machines

  36. Linear Sequential Machines

  37. Linear Sequential Machines

  38. Linear Sequential Machines

  39. Linear Sequential Machines

  40. A* = TAR B* = TB C* = CR D* = D Linear Sequential Machines

  41. Linear Sequential Machines

  42. Linear Sequential Machines

  43. Example 6: Minimize the linear machine given by following characterizing matrices A,B,C,D (Example Kohavi 15 - 20) Linear Sequential Machines

  44. Linear Sequential Machines

  45. Linear Sequential Machines

  46. Linear Sequential Machines

  47. Linear Sequential Machines

  48. A* = TAR B* = TB C* = CR D* = D Linear Sequential Machines

  49. Example 7: Minimize the linear machine given by following characterizing matrices A,B,C,D (Example Kohavi 15 - 21) Linear Sequential Machines

  50. Linear Sequential Machines

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