1. Signals and Systems Lecture Filter Structure and Quantization Effects

2. Implementation PART II

3. Structure for discrete-time

4. Realization of Filters

5. Digital Filter

6. Direct Form I Implementation

7. Block Diagram IIR DF-I

8. Realization of Filters: Ex.

9. Block Diagrams/ signal Flowgraphs

10. Signal Flow Graph: DF-I

11. Multiple Structures

12. Discrete Form II

13. Signal Flow Graph: IIR DF-II

15. Discrete Form II (canonic)

16. Cascade Form

17. Cascade Form: Real Case

18. IIR Cascade Form

19. Parallel Form

21. Transposed Forms

23. Structures for FIR Filters

25. Structures for LP FIR Filters

26. Quantization Effects  discrete-time filters, not digital filters.  Most DSP systems are implemented using fixed-point arithmetic  Floating-point arithmetic helps alleviate this problem, but consumes too much power and costs more  Due to the very nature of DSP, where digital data are obtained through an A/D converter, floating-point precision is usually not required

27. Coefficient Quantization  first design a discrete-time filter with double floating-point precision, such as the use of Matlab  Truncate (or round) the filter coefficients to implement the fixed- point HW/SW

28. Finite Precision effects

29. Quantization effects on the FIR systems

30. Unquantized FIR Filter Effect

31. 16-bit Quantization FIR Filter

32. 8-bit Quantization of FIR Filter

33. Finite Precision effects- Example

34. Coefficient Quantization

35. Coefficient Quantization(cont.)

36. DFII vs. 2 nd order sections for IIR

39. 2 nd Order Filter

40.   cos  and -  2 must be computed and rounded to the number of bits available  Suppose that we use a 4-bit quantizer b0.b1b2b3. Both  cos  and  2 can take on the numbers from 1.000 to 0.111 (-1 to 0.875)  Poles and zeros of a 2-nd order filter can only occur at the intersection of the lines representing  cos  and the semi-circles representing  2

41. Quantization in 2 nd order Section

42. Evenly Spaced Quantization  Non-uniform density of poles and zeros of a 2nd-order section can be mitigated by using a “coupled form” structure  The quantized poles and zeros are at the intersections of evenly spaced horizontal and vertical lines.