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Discrete-time Signal Processing Lecture 6 (Structures for discrete-time systems)

Husheng Li, UTK-EECS, Fall 2012. Discrete-time Signal Processing Lecture 6 (Structures for discrete-time systems). Study how to implement the LTI discrete-time systems. We first present the block diagram and signal flow graph.

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Discrete-time Signal Processing Lecture 6 (Structures for discrete-time systems)

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  1. Husheng Li, UTK-EECS, Fall 2012 Discrete-time Signal ProcessingLecture 6 (Structures for discrete-time systems)

  2. Study how to implement the LTI discrete-time systems. We first present the block diagram and signal flow graph. Then, we derive a number of basic equivalent structures for implementing a causal LTI. Purpose of this chapter

  3. The basic blocks include adders, scalars and delay registers. Block diagram representation

  4. A block diagram can be rearranged or modified without changing the overall system function. In the left system, the two cascading sub-systems can be reversed while the system function is still the same. Block diagram

  5. Direct forms I and II

  6. The graph representation consists of source, sink, intermediate nodes, additions, scalings and delays. Signal flow graph representation

  7. Basic structure for IIR: direct forms

  8. A variety of theoretically equivalent systems can be obtained by simply pairing the poles and zeros in different ways. When the computation precision is finite, the performance could be quite different for different realizations. IIR: cascading form

  9. We can express a rational system as a partial faction expansion and thus obtain the parallel form of an IIR. IIR: parallel form

  10. Transposition of a flow graph is accomplished by reversing the directions of all branches in the network while keeping the branch transmittances as they were and reversing the roles of the input and output. For SISO systems, the transposition does not change the system function. Transposed forms

  11. FIR: direct form Direct form Transposition

  12. Linear-phase FIR M is even M is odd

  13. The basic building block is called a two-port flow graph. The system is achieved by cascading the blocks. Lattice filters

  14. The coefficients of the filters can be determined by the coefficients-to-k-parameters algorithm. FIR Lattice filter

  15. A lattice structure for the all-pole system can be developed from FIR lattice by realizing that it is the inverse filter of an FIR system. All-pole Lattice structure

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