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EENG 751 3/16/20169-1 EENG 751: Signal Processing I Class # 9 Outline Signal Flow Graph Implementation l Fundamentals l System Function l Graph Construction.

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Presentation on theme: "EENG 751 3/16/20169-1 EENG 751: Signal Processing I Class # 9 Outline Signal Flow Graph Implementation l Fundamentals l System Function l Graph Construction."— Presentation transcript:

1 EENG 751 3/16/20169-1 EENG 751: Signal Processing I Class # 9 Outline Signal Flow Graph Implementation l Fundamentals l System Function l Graph Construction l Graph Analysis l Applications l Complex Coefficient Systems

2 EENG 751 3/16/20169-2 SFG Reference IEEE Transactions on Signal; Processing, vol 41 No. 3 March 1993 “Efficient Computation of the DFT with Only a Subset of Input or Output Points” page 1184.

3 EENG 751 3/16/20169-3 SFG Reference IEEE Transactions on Signal; Processing, vol 41 No. 3 March 1993 “Efficient Computation of the DFT with Only a Subset of Input or Output Points” page 1188.

4 EENG 751 3/16/20169-4 SFG Fundamentals

5 EENG 751 3/16/20169-5 SFG Fundamentals (Cont)

6 EENG 751 3/16/20169-6 SFG Fundamentals (Cont)

7 EENG 751 3/16/20169-7 SFG Fundamentals (Cont)

8 EENG 751 3/16/20169-8 SFG Generation

9 EENG 751 3/16/20169-9 SFG Generation (Cont)

10 EENG 751 3/16/20169-10 SFG Generation (Cont)

11 EENG 751 3/16/20169-11 SFG Generation (Cont)

12 EENG 751 3/16/20169-12 SFG Generation (Cont)

13 EENG 751 3/16/20169-13 SFG Generation (Cont)

14 EENG 751 3/16/20169-14 SFG Generation (Cont)

15 EENG 751 3/16/20169-15 SFG Generation (Cont)

16 EENG 751 3/16/20169-16 SFG Generation (Cont)

17 EENG 751 3/16/20169-17 SFG Generation (Cont)

18 EENG 751 3/16/20169-18 SFG Generation (Cont)

19 EENG 751 3/16/20169-19 SFG Application Reference IEEE Transactions on Signal; Processing, vol 41 No. 3 March 1993 “Efficient Computation of the DFT with Only a Subset of Input or Output Points” page 1188.

20 EENG 751 3/16/20169-20 SFG Application Reference IEEE Transactions on Signal; Processing, vol 41 No. 3 March 1993 “Efficient Computation of the DFT with Only a Subset of Input or Output Points” page 1189.

21 EENG 751 3/16/20169-21 SFG Application Example

22 EENG 751 3/16/20169-22 SFG Application Example

23 EENG 751 3/16/20169-23 SFG Application Example

24 EENG 751 3/16/20169-24 SFG Application Example

25 EENG 751 3/16/20169-25 SFG Application Example (Cont)

26 EENG 751 3/16/20169-26 Alternate Canonic Forms

27 EENG 751 3/16/20169-27 Alternate Canonic Forms (Cont)

28 EENG 751 3/16/20169-28 Alternate Canonic Forms (Cont)

29 EENG 751 3/16/20169-29 Alternate Canonic Forms (Cont)

30 EENG 751 3/16/20169-30 Alternate Canonic Forms (Cont)

31 EENG 751 3/16/20169-31 Cascade Form

32 EENG 751 3/16/20169-32 Cascade Form

33 EENG 751 3/16/20169-33 Parallel Form

34 EENG 751 3/16/20169-34 Parallel Form (Cont)

35 EENG 751 3/16/20169-35 The Transposition Theorem

36 EENG 751 3/16/20169-36 The Transposition Theorem (Cont)

37 EENG 751 3/16/20169-37 The Transposition Theorem (Cont)

38 EENG 751 3/16/20169-38 FIR Filter Equations

39 EENG 751 3/16/20169-39 Transpose FIR Filter Equations

40 EENG 751 3/16/20169-40 The Transposition Theorem (Cont)

41 EENG 751 3/16/20169-41 FIR SFGs

42 EENG 751 3/16/20169-42 FIR SFGs (Cont)

43 EENG 751 3/16/20169-43 FIR SFGs (Cont)

44 EENG 751 3/16/20169-44 FIR SFGs (Cont)

45 EENG 751 3/16/20169-45 FIR SFGs (Cont)

46 EENG 751 3/16/20169-46 FIR SFGs (Cont)

47 EENG 751 3/16/20169-47 Linear Phase FIR SFGs

48 EENG 751 3/16/20169-48 Linear Phase FIR SFGs (Cont)

49 EENG 751 3/16/20169-49 Linear Phase FIR SFGs (Cont)

50 EENG 751 3/16/20169-50 Causal Linear Phase Systems

51 EENG 751 3/16/20169-51 Causal Linear Phase Systems (Cont)

52 EENG 751 3/16/20169-52 Causal Linear Phase Systems (Cont)

53 EENG 751 3/16/20169-53 Causal Linear Phase Systems (Cont)

54 EENG 751 3/16/20169-54 Causal Linear Phase Systems (Cont)

55 EENG 751 3/16/20169-55 Causal Linear Phase Systems (Cont)

56 EENG 751 3/16/20169-56 Linear Phase FIR SFGs (Cont)

57 EENG 751 3/16/20169-57 Linear Phase FIR SFGs (Cont)

58 EENG 751 3/16/20169-58 Linear Phase FIR SFGs (Cont)

59 EENG 751 3/16/20169-59 Linear Phase FIR SFGs (Cont)

60 EENG 751 3/16/20169-60 Linear Phase FIR SFGs (Cont)

61 EENG 751 3/16/20169-61 Linear Phase FIR SFGs (Cont)

62 EENG 751 3/16/20169-62 Linear Phase FIR SFGs (Cont)

63 EENG 751 3/16/20169-63 Linear Phase FIR SFGs (Cont)

64 EENG 751 3/16/20169-64 Linear Phase FIR SFGs (Cont)

65 EENG 751 3/16/20169-65 Linear Phase FIR SFGs (Cont)

66 EENG 751 3/16/20169-66 Linear Phase FIR SFGs (Cont)

67 EENG 751 3/16/20169-67 All Pass Filters

68 EENG 751 3/16/20169-68 All Pass Filters (Cont)

69 EENG 751 3/16/20169-69 All Pass Filters (Cont)

70 EENG 751 3/16/20169-70 All Pass Filters (Cont)

71 EENG 751 3/16/20169-71 All Pass Filters (Cont)

72 EENG 751 3/16/20169-72 All Pass Filters (Cont) Consider the second SFG Flip it over I.e. Pull down I.e.

73 EENG 751 3/16/20169-73 All Pass Filters (Cont)

74 EENG 751 3/16/20169-74 All Pass Filters (Cont)

75 EENG 751 3/16/20169-75 Signal Flow Graph Example

76 EENG 751 3/16/20169-76 Signal Flow Graph Example (Cont)

77 EENG 751 3/16/20169-77 Signal Flow Graph Example (Cont)

78 EENG 751 3/16/20169-78 Signal Flow Graph Example (Cont)

79 EENG 751 3/16/20169-79 Signal Flow Graph Example (Cont)

80 EENG 751 3/16/20169-80 Signal Flow Graph Example (Cont)

81 EENG 751 3/16/20169-81 Signal Flow Graph Example (Cont)

82 EENG 751 3/16/20169-82 Signal Flow Graph Example (Cont)

83 EENG 751 3/16/20169-83 Exercise (To be Handed In)

84 EENG 751 3/16/20169-84 Complex Filter Example

85 EENG 751 3/16/20169-85 Complex Filter Example(Cont)

86 EENG 751 3/16/20169-86 Complex System Signal Flow Graphs

87 EENG 751 3/16/20169-87 Complex System SFG(Cont)

88 EENG 751 3/16/20169-88 Complex System Signal Flow Graphs

89 EENG 751 3/16/20169-89 Application from IEEE Transactions on Signal Processing, Vol 46, No.2 Feb 98 Page 364

90 EENG 751 3/16/20169-90 Application from IEEE Transactions on Signal Processing, Vol 46, No.2 Feb 98 Page 368

91 EENG 751 3/16/20169-91 Application Example (Continued)

92 EENG 751 3/16/20169-92 Application Example (Continued)

93 EENG 751 3/16/20169-93 Application Example (Continued)

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