1. EEE4176 Applications of Digital Signal Processing
Fall 2011
Assistant Prof. Yangmo Yoo
Dept. of Electronic Engineering
Sogang University

2. Lecture 3: Multirate Signal Processing

3. Summary
M-fold Decimation:

4. Summary
L-fold Expansion: F1
L*F1
F1/M

5. Summary
x2(n)

6. Summary Efficient structures for decimation and interpolation filters
Decimation filter: M=2
Direct implementation
Polyphase implementation: Type 1
N+1 multiplications and N additions
at Fs
(N+1) MPUs and N APUs
During the odd clock cycles, resting Fs
Fs/2 n0 n1
N+1=n0+n1+2 multiplications
and N additions at Fs/2
= (N+1)/2 multiplications
and N/2 additions at Fs
(N+1)/2 MPUs and N/2 APUs
Due to noble identity

7. Summary Efficient structures for decimation and interpolation filters
Interpolation filter: L=2
Direct implementation
Polyphase implementation: Type 2 Fs
2Fs 2
2(N+1) MPUs and 2N APUs
Half of the samples are zero
(N+1) MPUs and (N-1) APUs

8. Summary
Ex: M=3, L=2 ; M/L = 1.5 M L
H(z)

9. Summary
Ex: M=3, L=2 ; M/L = 1.5

10. Lecture 3: Multistage Signal Processing10

11. Multistage Implementations
Multistage schemes
Lower rate operation
Lower computation amount: Simple filter spec
Multistage decimation 11

12. Multistage Implementations12

13. Multistage Implementations
Multistage Expansion (or interpolation) 13

14. Multistage Implementations
Motivation of multistage implementation
Length of a linear phase FIR filter
Multistage implementation helps to reduce the overall filter length 14

15. Multistage Implementations
IFIR (Interpolated FIR) approach
Model filter
H(z)
Image suppressor 15

16. Multistage Implementations
IFIR (Interpolated FIR) approach
Optimum # of stages ?
Neuvo. Et al. [1984] 16

17. Multistage Implementations
Multistage design of decimation filter
Design example 4.4.2 17

18. Multistage Implementations
Multistage design of decimation filter
Design example 4.4.2
symmetric
as M1 18

19. Multistage Implementations
Multistage design of decimation filter 19

20. Multistage Implementations
Multistage design of interpolator 20

21. Applications of Multirate systems
Digital audio
A/D
D/A
Fractional sampling rate conversion
Studio: 48KHz
CD mastering: 44.1KHz
Broadcasting: 32KHz
48K K :
L=441, M=480 21

22. Applications of Multirate systems
Subband coding of speech and image signals
DPCM, ADPCK: Jayant and Noll, 1984
Image compression: subband coding
Woods and O’Neil, 1986
Smith and Eddins, 1990
Woods, 1990
Music signals: DCC
Veldhuis, et al., 1989
pp , ICASSP, 1991
Fettweis, et al., 1990 22

23. Applications of Multirate systems
Analog voice privacy systems
Multirate adaptive filters
Transmultiplexers
Shynk [1992]
Time domain multiplexing
Demultiplexing 23

24. Applications of Multirate systems
Transmultiplexer structure 24

25. Applications of Multirate systems
Transmultiplexer structure 25

26. Lecture 3: Supplements Multistage Conversion
Dr. Mark Fowler from SUNY, EE512

27. Motivation for Multistage Schemes

28. Trick to Get Efficiency from Multistage

29. Why for a 2-Stage Case?

30. Why for a 2-Stage Case?

31. Why for a 2-Stage Case?

32. Design Requirements

33. Example: How 2-Stage Reduces Computation

34. Example: Single-Stage Method

35. Double-Stage Method

36. Comments on Multistage Method

37. Application: Multistage Rate Change