???? memory ? memory reference ?? ????? ???? FFT ??? ????? DSP

1

• ???? memory ? memory reference ?? ????? ???? FFT
  ??? ????? DSP
• ????? ??? ???? ??????
• ????? ????? ???? ?????? 810188169
• ???? 89

Class presentation for the course Custom
Implementation of DSP Systems All the materials
are copy rights of their respective authors as
listed in references.
2

• ???? ?????
• DFT
• ????? ???????? ??? ???? FFT
• ????? ????? ???? ???????? ??? FFT
• Memory reference ?? ????? ???? FFT ??? DSP??
• ????? FFT ?? memory reference ???? ?????
• ???? ????? twiddle factor ???? ???? ???? ????? ??
  ?????
• ?????? ??? ???????? ??? ????? ????
• ????? ?????

3

• DFT
• ?????? DFT ?? ????
  ???.
• ? Twiddle factor
  ?? ????.
• ???? ?????? ?????? DFT ???? ??? ??? ????? ?
  ??? ????? ????? ????. ?? ????? ????
  N??? ???? ?????? ?????? ???????? ???.
• ???????? ??? ???? ???? ?????? DFT? FFT ?????? ??
  ???.

4

• ???????? ??? ???? FFT
• radix-2 FFT
• Decimation In Time (DIT)
• Decimation In Frequency (DIF)
• higher radix FFT
• mixed radix FFT
• recursive FFT
• prime factor FFT

5

• ???????? DIT
• ???
  ?? ?????? ????
• 5

6

• ???????? DIT
• ?? ??? ???? ?? ??? ??? ? ???
  ????? ???? ?????.
• ????? ??????
  ?? DFT? N ???? ?? ?? ?? DFT? N/2 ???? ?? 5

7

• ???????? DIT
• ???? ????? ?? ???? ???? ???

8

• ???????? DIT
• ????? ??????
  ?? DFT? N ???? ?? ?? ???? DFT? N/4 ???? ?? 5

9

• ???????? DIT
• ?? ????? ??? ???? ??????? ?????? DFT ?? ???? ???
  ??? ????? ???.
• ??????? ?????? ?????? ???? 5
  ???????
  ????? ???? DIT ?? ?????? DFT ?? 8 ???? 5

10

• ????? ????? ???? ???????? ??? FFT
• ?? ???? ASIC
• ???? GPP??
• ???? DSP??

11

• Memory reference ?? ????? ???? FFT ??? DSP??
• ????? ???? memory reference
• 
  ??????? FFT? DIT 16 ???? ?? 2

12

• Memory reference ?? ????? ???? FFT ??? DSP??
• 
  ??????? FFT? DIF 16 ???? ?? 2

13

• FFT ?? memory reference ???? ?????
• ???? ???? ?????? ??
• ??????? FFT? DIT ?? DIF ???? ???? ??
  ?? ???? N/2 ?????? ?????.
• ?????? ??? ????? ?? ???? s DIT FFT ??
  ???? ????? ???? ?? ????.
• ???? ???? ???? ?????? ?? ?? FFT?
  DIT 16 ???? ?? 2

14

• FFT ?? memory reference ???? ?????
• ?????? ??? ????? ?? ???? s ?? DIF FFT ??
  ???? ????? ???? ?? ????.
• ???? ???? ???? ?????? ?? ?? FFT? DIF 16
  ???? ?? 2

15

• FFT ?? memory reference ???? ?????
• ?? ???? S ??????? DIF FFT? N ???? ?? ?? ?????
  twiddle factor ????? ???? ???? ?? ?? ????
  ???? ???? ??? ?? .
• ?? ??? ????? twiddle factor??? ?? ???
  ?? ?? ????? ???? ????
  ??????.

16

• FFT ?? memory reference ???? ?????
• ?? ????? ???? ??
  ??????? ????? ??? ?? ???? ??? ???? ????? ?
  ?? ????? ??? ?? ???? ?? ???? ??????.
• ??????? FFT? DIF 16
  ???? ?? 2

17

• FFT ?? memory reference ???? ?????
• ????????
• Step 1 ?????? ?????? ???? ?? twiddle factor????
  ?? ?? ????? ??? ?? 1 ????? ??? ????. N/4 ??????
  ??? ????? ?? ???? 1 ?? ????? twiddle factor ??
  ???? ?? ????? ??
  ??? Step ?????? ?? ????.
• Step 2 ?????? ?????? ???? ?? twiddle factor????
  ?? ?? ????? ??? ?? 2 ????? ??? ????. ????? ??????
  ???? ?? ?? ??? step ???? ?????? ???? ?? ????? N/4
  ?? ?????? ??? ???? 2 ? N/8 ?? ?????? ??? ???? 1
  ????? ?? twiddle factor ???? ?? ???? ????? ???
  ??

18

• FFT ?? memory reference ???? ?????
• ????????
• Step s ?????? ?????? ???? ?? twiddle factor????
  ?? ?? ????? ??? ?? s ????? ??? ????. ????? ??????
  ???? ?? ?? ??? step ???? ?????? ???? ?? ????? N/4
  ?? ?????? ??? ???? s ? N/8 ?? ?????? ??? ???? 1-
  s? ... ? ?? ???? ??? ????? ?? twiddle
  factor ???? ?? ???? ????? ??? ??
• Step ?? ??? step ?????? ???? ??
  twiddle factor ???? ?? ???? ??????
• ?? ???? ?? ????? ???? ????? 1-N ???.

19

• FFT ?? memory reference ???? ?????
• ???????
  DIF FFT ?? ?? ???? memory reference ???? ?????
  ???. 2

20

• FFT ?? memory reference ???? ?????
• 
  ??????? DIT FFT ?? ?? ???? memory reference ????
  ????? ???. 2

21

• FFT ?? memory reference ???? ?????
• ???? ?????? DFT??? ???? ??? ??? ?? cash ?????
  ?????? ????.
• 
  ????? ???? ?????? ?? ?? FFT ???
  ?????? 1

22

• ???? ????? twiddle factor ???? ???? ???? ????? ??
  memory
• ?? ???? ????? ??? twiddle factor ?????
• ????

23

• ???? ????? twiddle factor ???? ???? ???? ????? ??
  memory
• FFT??? 16 ???? ?? ????? ?? 7 twiddle factor
  ??????? ?? ??? ??? ?? ??? ???? ????? 2 ?? 3
  twiddle factor ??????? ?? ???.
• 
  ????? twiddle factor ??? ???? ????? 2 ?
  ?????. 1

24

• ???? ????? twiddle factor ???? ???? ???? ????? ??
  memory
• ??????? DIF FFT? 16 ????
  ?? memory reference ???? ????? ??? ?? ???? ?????
  twiddle factor. 2

25

• ???? ????? twiddle factor ???? ???? ???? ????? ??
  memory
• ??????? DIT FFT? 16 ????
  ?? memory reference ???? ????? ??? ?? ???? ?????
  twiddle factor. 2

26

• ???? ????? twiddle factor ???? ???? ???? ????? ??
  memory
• 
  ???? ????? twiddle factor ?? radix-4 DIF FFT? 16
  ???? ?? 2

27

• ???? ????? twiddle factor ???? ???? ???? ????? ??
  memory
• 
  ????? ??? ????? sin ? cos ? ???? ????? ?????
  twiddle factor??. 1

28

• ?????? ??? ???????? ??? ????? ????
• ????
  ???? ?? 1

29

• ?????? ??? ???????? ??? ????? ????
• ???????? ?? CPU ?? ???? ??????? ?? ????? ????
  ????? ??? ???. 1

30

• ????? ?????
• 1. Tsung-Ying Sun, And Yu-Hsiang Yu, Memory
  Usage Reduction Method for FFT Implementations on
  DSP Based Embedded System, IEEE conf.
  International Symposium on Consumer Electronics,
  July 2009.
• 2. Y. Wang, Y. Tang, Y. Jiang, J.G. Chung, S.S.
  Song, and M.S. Lim, Novel Memory Reference
  Reduction Methods for FFT Implementations on DSP
  Processors, IEEE Trans. Signal Processing, vol.
  55, no. 5, pp. 2338-2349, MAY 2007.
• 3. Yi-Pin Hsu and Shin-Yu Lin, Implementation of
  Low-Memory Reference FFT on Digital Signal
  Processor, Journal of Computer Science 4 (7)
  547-551, 2008.
• 4. Yi-Pin Hsu, and Shin-Yu Lin,
  Parallel-computing approach for FFT
  implementation on digital signal processor
  (DSP), World Academy of Science, Engineering and
  Technology 42, 2008.
• 5. Oppenheim, A.V., and R.W. Schafer.
  Discrete-Time Signal Processing. 2nd Edition,
  Prentice Hall, 1999