1. Lattice Struture

2. Lattice structure Lattice structure for FIR filter Difference equation
Linear prediction
(6-64)
(6-65)
(6-66)
Error between and
FIR filter uses linear predictor
(6-67)
where is prediction coefficient

3. For N=1 Single-stage FIR lattice structure
(6-68)
(6-69)
where is reflection coefficient
Fig

4. For N=2
(6-70)
Fig

5. For N=3
Substituting
(6-71)
Fig

6. For N=M If
(6-72)
where
(6-73)
(6-74)

7. Fig

8. Example 6-15
(1)

9. (2) Calculation of coefficients
From Fig and Eq. (6-73)
(6-75)
Fig

10. Calculation of filter coefficient From Eq. (6-75)
m-stage
(6-76)
(6-77)
Substituting
(6-78)

11. For
(6-79)
Substituting in Eq. (6-74)
(6-80)

12. Example 6-16
from example 6-15

13. General form of calculating filter coefficient
From Eq. (6-73)
Substituting M=m
Substituting z=1/z
(6-81)
(6-82)
(6-83)
(6-84)

14. For

15. In Eq. (6-80)
Substituting and
(6-85)

16. Dividing by
Coefficient
(6-86)

17. Example 6-17

18. Calculating coefficient of
For

19. For

20. from Eq. (6-86)

21. Fig

22. Lattice structure of IIR filter
All-pole system
Difference equation
(6-87)
(6-88)
(6-89)
(6-90)

23. For N=1
(6-91)
Fig

24. For N=2
(6-92)
Fig

25. For N th order
(6-93)
Fig

26. General form of IIR system
Lattice-ladder structure
(6-94)
All-pole lattice structure
Ladder structure

27. Lattice-ladder structure System output
Transfer function
(6-95)
(6-96)

28. From Eq. (6-94) and (6-96)
(6-97)
where
(6-98)

29. Fig

30. Example 6-18
All-pole system
Fig

31. Example 6-19
Equation for each node

32. Comparison of coefficients

33. Fig

34. Introduction of digital filter
Real-time digital filter with analog input and output signal
Sampling the bandlimited analog signal periodically
Converting into a series of digital samples
Implementation of the filtering operation in digital processor
Mapping the input sequence into the output sequence
Converting the digitally filtered output into analog values by using DAC
Smoothing and removing unwanted high frequency components
Fig

35. Advantage of digital filter compared with analog filters
A truly linear phase response
The performance of digital filters does not vary with environmental change
The frequency response of a digital filter can be automatically adjusted if it is implemented using a programmable processor
Several input signals or channels can be filtered by one digital filter without the need to replicate the hardware
Both filtered and unfiltered data can be saved for further use

36. Miniaturization and low power consumption by VLSI
The precision achievable with analog filters is restricted
The performance of digital filters is repeatable from unit to unit
Digital filters can be used at very low frequencies

37. Disadvantage of digital filters compared with analog filters
Speed limitation
Finite wordlength effect
Long design and development times

38. Types of digital filters : FIR and IIR filters
FIR filter
(6-99)
(6-100)

39. IIR filtering equation of recursive form
Alternative representations for FIR and IIR filters
Transfer function
where and are coefficients of filter
IIR is feedback system of some sort
(6-102)
(6-103)

40. Choosing between FIR and IIR filters
Relative advantages of the two filter types
FIR filters can have an exactly linear phase response
FIR filters are always stable. The stability of IIR filters cannot always be guaranteed
The effect of using a limited number of bits to implement filters
Roundoff noise and coefficient quantization errors are much less severe in FIR than in IIR
FIR requires more coefficients for sharp cutoff filters than IIR
Analog filters can be readily transformed into equivalent IIR digital filters meeting similar specifications
In general, FIR is algebraically more difficult to synthesize

41. Guideline on when to use FIR or IIR
Use IIR when the only important requirements are sharp cutoff filters and high throughput
Use FIR if the number of filter coefficients is not too large and, in particular, if little or no phase distortion is desired