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Chapter 6 Discrete-Time System

Chapter 6 Discrete-Time System. 1. Discrete time system. Operation of discrete time system. where and are multiplier D is delay element. Fig. 6-1. 2. Difference equation. Difference equation. where and is constant or function of n. Example 6-1 Moving average

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Chapter 6 Discrete-Time System

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  1. Chapter 6 Discrete-Time System

  2. 1. Discrete time system • Operation of discrete time system where and are multiplier D is delay element Fig. 6-1.

  3. 2. Difference equation • Difference equation where and is constant or function of n

  4. Example 6-1 • Moving average • Example 6-2 • Integration If If

  5. 3. Linear time-invariant system • Functional relationship of discrete time system Fig. 6-2. where is impulse response of system

  6. The system is said to be linear if • The system is said to be time-invariant if

  7. Form and transfer function • Difference equation of discrete time system After z-transform

  8. Transfer function If where is impulse response of system

  9. Impulse response of discrete time system If is power series In this case,

  10. Example 6-3 Using power series

  11. Using other method Substitute , and initial value

  12. Example 6-4 Using z-transfrom Using inverse z-transfrom

  13. If initial value Using inverse z-transfrom

  14. System stability • BIBO(bounded input, bounded output)

  15. Raible tabulation Table 6-1. Raible’s tabulation

  16. If part or all factor is 0 in the first row, then this table is ended • Singular case • Using substitution n th order case

  17. Example 6-5

  18. Example 6-6

  19. Singular case

  20. Example 6-7

  21. 4. Description of Pole-Zero • Discrete time system transfer function H(z) where K is gain Poles of at : Zeros of at :

  22. Description of pole and zero in z-plane Fig. 6-3.

  23. Example 6-8 Fig. 6-4.

  24. Example 6-9 Fig. 6-5. K=0.2236

  25. 5. Frequency response • Frequency response of system • Method for calculation • Method for geometric calculation

  26. Example 6-10 • Method for calculation • Substitution of and using Euler’s formular

  27. Substitution of

  28. Fig. 6-6.

  29. Method for geometric calculation Magnitude response Phase response Fig. 6-7.

  30. 6. Realization of system Unit delay Adder/subtractor Constant multiplier Branching Signal multiplier Fig. 6-8.

  31. Direct form • Direct form 1

  32. (a) (b) Fig. 6-9.

  33. Direct form 2 Inverse transform poles zeros

  34. (a) (b) Fig. 6-10.

  35. Example 6-11 • Direct form 1 • Direct form 2

  36. (a) (b) Fig. 6-11.

  37. Quantization effect of parameters • Quantization error of parameters • Input signal quantization • Accumulation of arithmetic roundoff errors • Coefficient of transfer function quantization

  38. Cascade and parallel canonic form • Cascade canonic form or series form first order second order

  39. Fig. 6-12. (a) (b) Fig. 6-13.

  40. Parallel canonic form first order second order

  41. Fig. 6-14.

  42. (a) (b) Fig. 6-15.

  43. Example 6-12 • Cascade canonic form Quantization error of parameter is decreased

  44. Parallel canonic form

  45. (a) (b) Fig. 6-16.

  46. Example 6-13 Fig. 6-17.

  47. Example 6-14 Substitute

  48. Fig. 6-18.

  49. FIR system • Direct form • Tapped delay line structure or transversal filter Fig. 6-19.

  50. Cascade canonic form where Fig. 6-20.

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