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Part 5 Response of Linear Systems

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Part 5 Response of Linear Systems

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    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

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