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Martijn v/d Horst M.G.v.d.Horst@tue.nl

Parallel Implementation of IIR Filters. Martijn v/d Horst M.G.v.d.Horst@tue.nl. Outline. IIR Filters Implementation Methods Look Ahead Block-State Incremental Block-State Extra buffer Comparison All-pass Filters Conclusion and Future Work. Input. Output. IIR Filters.

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Martijn v/d Horst M.G.v.d.Horst@tue.nl

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  1. Parallel Implementation of IIR Filters Martijn v/d Horst M.G.v.d.Horst@tue.nl

  2. Outline • IIR Filters • Implementation Methods • Look Ahead • Block-State • Incremental Block-State • Extra buffer • Comparison • All-pass Filters • Conclusion and Future Work

  3. Input Output IIR Filters

  4. Describing Filters • Transfer Function: • Difference Equation: • State space form:

  5. Implementation We want: • Sample rates exceeding processing rates • This means parallel inputs and outputs, also called block implementations • Implementations which scale well

  6. Clustered Look Ahead • Increase the size of the recursive loop • The order of the filter increases • Might become unstable n-2 n-1 n n n-P-1 n-P P

  7. Scattered Look Ahead • Increase the size of the recursive loop • The order of the filter increases • Remains stable • Can be implemented with P parallel filters • Non-recursive part can be decomposed n-2 n-1 n n-2P n-P n P P

  8. Block-State The state space form can be rewritten into a state space form using input and output vectors:

  9. Block-State Architecture Input State Output

  10. State update

  11. Block-State

  12. Incremental Block-State

  13. Output Output State State Extra buffer • Transform a Mealey into a Moore Machine • Filter order increases by one • P - 1 multipliers saved for Block-State • P - P div I multipliers saved for Incremental Block-State

  14. Comparison Efficiency: The number of multipliers used by an implementation compared to the theoretical optimum number. A single input, single output implementation of an IIR filter of order N requires 2 N + 1 multipliers. Therefore the theoretical optimum for an implementation handling P simultaneous inputs and outputs is P (2 N + 1) multipliers.

  15. Efficiencies Scattered Look ahead Block-state Incremental Block-state with extra buffer Incremental Block-state

  16. Efficiencies N=8 N=16 Scattered Look ahead Block-state N=32 N=64 Incremental Block-state Incremental Block-state with extra buffer

  17. All-pass Filters • Also called phase shifters • Theoretical optimum is P N

  18. Conclusion • Efficient block implementations for IIR filters exist • These implementations can be used for all-pass filters • Theoretically there is room for improvement in implementing all-pass filters

  19. Future Work • Finding more efficient all-pass implementations • Adaptive Equalizers • Other signal processing algorithms

  20. Questions?

  21. Farewell Thang

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