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 transcript:

EENG 751 3/16/ 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

EENG 751 3/16/ 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.

EENG 751 3/16/ 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.

EENG 751 3/16/ SFG Fundamentals

EENG 751 3/16/ SFG Fundamentals (Cont)

EENG 751 3/16/ SFG Fundamentals (Cont)

EENG 751 3/16/ SFG Fundamentals (Cont)

EENG 751 3/16/ SFG Generation

EENG 751 3/16/ SFG Generation (Cont)

EENG 751 3/16/ SFG Generation (Cont)

EENG 751 3/16/ SFG Generation (Cont)

EENG 751 3/16/ SFG Generation (Cont)

EENG 751 3/16/ SFG Generation (Cont)

EENG 751 3/16/ SFG Generation (Cont)

EENG 751 3/16/ SFG Generation (Cont)

EENG 751 3/16/ SFG Generation (Cont)

EENG 751 3/16/ SFG Generation (Cont)

EENG 751 3/16/ SFG Generation (Cont)

EENG 751 3/16/ 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.

EENG 751 3/16/ 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.

EENG 751 3/16/ SFG Application Example

EENG 751 3/16/ SFG Application Example

EENG 751 3/16/ SFG Application Example

EENG 751 3/16/ SFG Application Example

EENG 751 3/16/ SFG Application Example (Cont)

EENG 751 3/16/ Alternate Canonic Forms

EENG 751 3/16/ Alternate Canonic Forms (Cont)

EENG 751 3/16/ Alternate Canonic Forms (Cont)

EENG 751 3/16/ Alternate Canonic Forms (Cont)

EENG 751 3/16/ Alternate Canonic Forms (Cont)

EENG 751 3/16/ Cascade Form

EENG 751 3/16/ Cascade Form

EENG 751 3/16/ Parallel Form

EENG 751 3/16/ Parallel Form (Cont)

EENG 751 3/16/ The Transposition Theorem

EENG 751 3/16/ The Transposition Theorem (Cont)

EENG 751 3/16/ The Transposition Theorem (Cont)

EENG 751 3/16/ FIR Filter Equations

EENG 751 3/16/ Transpose FIR Filter Equations

EENG 751 3/16/ The Transposition Theorem (Cont)

EENG 751 3/16/ FIR SFGs

EENG 751 3/16/ FIR SFGs (Cont)

EENG 751 3/16/ FIR SFGs (Cont)

EENG 751 3/16/ FIR SFGs (Cont)

EENG 751 3/16/ FIR SFGs (Cont)

EENG 751 3/16/ FIR SFGs (Cont)

EENG 751 3/16/ Linear Phase FIR SFGs

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

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

EENG 751 3/16/ Causal Linear Phase Systems

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

EENG 751 3/16/ All Pass Filters

EENG 751 3/16/ All Pass Filters (Cont)

EENG 751 3/16/ All Pass Filters (Cont)

EENG 751 3/16/ All Pass Filters (Cont)

EENG 751 3/16/ All Pass Filters (Cont)

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

EENG 751 3/16/ All Pass Filters (Cont)

EENG 751 3/16/ All Pass Filters (Cont)

EENG 751 3/16/ Signal Flow Graph Example

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

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

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

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

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

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

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

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

EENG 751 3/16/ Complex Filter Example

EENG 751 3/16/ Complex Filter Example(Cont)

EENG 751 3/16/ Complex System Signal Flow Graphs

EENG 751 3/16/ Complex System SFG(Cont)

EENG 751 3/16/ Complex System Signal Flow Graphs

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

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

EENG 751 3/16/ Application Example (Continued)

EENG 751 3/16/ Application Example (Continued)

EENG 751 3/16/ Application Example (Continued)