Part 5 Response of Linear Systems

1. 1

2. 2 6. Linear Filtering of a Random Signal Linear System Our goal is to study the output process statistics in terms of the input process statistics and the system function.

3. 3 Deterministic System

4. 4 Memoryless Systems

5. 5 Linear Time-Invariant Systems

6. 6 Linear Filtering of a Random Signal

7. 7 Theorem 6.1

8. 8 Theorem 6.2

9. 9 Theorem 6.2 (Cont’d)

10. 10 Example 6.1

11. 11 Example 6.2

12. 12 Theorem 6.3

13. 13 Example 6.3

14. 14 Theorem 6.4

15. 15 Example 6.4

16. 16 Theorem 6.5

17. 17 Example 6.5

18. 18 Example 6.6

19. 19 Example 6.7

20. 20 Example 6.8

21. 21 Theorem 6.6

22. 22 Example 6.9

23. 23 Example 6.10

24. 24

25. 25 7. Power Spectrum Analysis

26. 26 Theorem 7.1

27. 27 Theorem 7.2

28. 28 Example 7.1

29. 29 Example 7.2

30. 30 Discrete-Time Fourier Transform (DTFT)

31. 31 Power Spectral Density of a Random Sequence

32. 32 Theorem 7.4

33. 33 Example 7.4

34. 34 Example 7.5

35. 35 Cross Spectral Density

36. 36 Example 7.6

37. 37 Example 7.7

38. 38 Frequency Domain Filter Relationships

39. 39 Theorem 7.5

40. 40 Example 7.8

41. 41 Example 7.9

42. 42 Example 7.10

43. 43 Theorem 7.6

44. 44 I/O Correlation and Spectral Density Functions

45. 45

46. 46 8. Linear Estimation and Prediction Filters

47. 47 Linear Prediction Filters

48. 48 Theorem 8.1

49. 49 Example 8.1

50. 50 Theorem 8.2

51. 51 Linear Estimation Filters

52. 52 Theorem 8.3

53. 53 Example 8.2

54. 54

55. 55 9. Mean Square Estimation

56. 56 Theorem 9.1:Linear Estimation

57. 57 Example 9.1