1. 1 95-1 Under-Graduate Project Adviser: Prof. An-Yeu Wu Mentor: 詹承洲 第二組 溫仁揚 溫昌懌

2. 2 Outline Purpose of fixed-point Analysis Fixed-point C model Simulation by C language RTL model Conclusion Future work Reference

3. 3 Purpose of Fixed-Point Analysis Simulate hardware implementation Quantization Choose the best allocation of bits

4. 4 Fixed-Point C Model quantization saturation truncation Work point:

5. 5 Fixed-Point C Model In every clock : 3456789 64 point

6. 6 Fixed-Point C Model Floating point Exactly the value Hard for hardware implementation Fixed point Quantization Truncation 、 saturation Easy for hardware implementation

7. 7 Fixed-Point C Model S=1 Take fixed number: Can reduce ½ of error errorerror signal caused by the quantization!quantization The following C model apply the first method

8. 8 Fixed-Point C Model Requirement: Number of bits for input data: 10~14 Number of bits for output data: 16~20 Dynamic range for input data: [-4 4] Integer part of input data: 3~10 fractional part of input data: 3~10 Twiddle factor: 6~13 SQNR ≥ 50dB

9. 9 Fixed-Point C Model SQNR: Signal-to-Quantization-Noise Ratio SNR (S/N) : Signal-to Noise Ratio

10. 10 Fixed-Point C Model Note that for each bit added to a sample, the SQNR goes up by about 6dB. xxx.xooo : max error < 0.25 xxx.xxoo : max error < 0.125 10log4≈6 ½

11. 11 Simulation by C Language(1/9) Wordlength Simulation: fractional=10 Integer=6 Twiddle factor word length Integer word length SQNR: Average of 10 points

12. 12 Simulation by C Language(2/9) Wordlength Simulation: twiddle factor=13 Integer=6 SQNR: Integer wordlength Fractional wordlength Average of 10 points

13. 13 Simulation by C Language(3/9) Critical value Take integer wordlength=6 Analyze:

14. 14 Simulation by C Language(4/9) Wordlength Simulation: integer =6 SQNR: Twiddle factor wordlength Fractional wordlength Fractional=10 t.f=10 Fractional=9 t.f=11 Average of 100 points

15. 15 Simulation by C Language(5/9) Wordlength Simulation: integer =5 T.F wordlength Frac. wordlength Average of 100 points SQNR: Wordlength Simulation: integer =7 T.F wordlength Frac. wordlength

16. 16 Simulation by C Language(6/9) Word length Simulation: integer =6 Twiddle factor wordlength Fractional wordlength Variance: Average of 50 points

17. 17 Simulation by C Language(7/9) With larger wordlength,there should be smaller variance But some area are not Should take more point number

18. 18 Simulation by C Language(8/9) Wordlength Simulation: integer =6 Twiddle factor wordlength Difference of SQNR : Wordlength Simulation: integer =7 Difference of SQNR : Fractional wordlength Twiddle factor wordlength Fractional wordlength T.F = 7 Average of 20 points Difference by twiddle factor: T.F = 10

19. 19 Simulation by C Language(9/9) Should be only one maximum Should take enough point number

20. 20 Conclusion: Work point: Integer =6 Fractional=10 t.f=10 or Integer =6 Fractional=9 t.f=11 Fractional =7 has the best performance when other variable

21. 21 RTL model lib.v main.v Connect the lines

22. 22 Lib.v module BF2ii(Zar,Zai,Zbr,Zbi,Xar,Xai,Xbr,Xbi,s,t); module BF2i(Zar,Zai,Zbr,Zbi,Xar,Xai,Xbr,Xbi,s); Already tested successfully.

23. 23 Main.v Still need to work on it.

24. 24 Future work: RTL code to be completed Search for better performance Synthesis circuit

25. 25 Reference ： Shousheng He & Torkelson, M., ” A new approach to pipeline FFT processor, ” Proceedings of IPPS ’ 96, 15-19 April 1996, pp766- 770. 施信毓, ” 95-1 Under-Graduate Project, Final Project: Fixed_point ”,08 Dec 2006. http://en.wikipedia.org/ http://zh.wikipedia.org/