# Compare ideal Interpolation filter and interpolation by LSE FIR filter(Final) Advisor : Dr. Yung-AN Kao Student: Ying Chun Chen.

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Compare ideal Interpolation filter and interpolation by LSE FIR filter(Final) Advisor : Dr. Yung-AN Kao Student: Ying Chun Chen

Outline Kaiser Window Comparison (Simulation) Conclusion & Future work Reference

Kaiser Window

Kaiser Window (Simulation) Filter coefficient M=65 Cutoff freq=0.2  1 st Passband freq=0.15  1 st Stopband freq=0.25  1 st Delta=0.002 2 nd Passband freq=0.1  2 nd Stopband freq=0.3  2 nd Delta=1.0133*10 -5 3 rd Passband freq=0.17  3 rd Stopband freq=0.23  3 rd Delta=0.016662

Comparison(1/14) Filter coefficient M=65 Interpolation filter by Kaiser Window Upsample=5 Cutoff freq=0.2  1 st Passband freq=0.1  1 st Stopband freq=0.3  2 nd Passband freq=0.17  2 nd Stopband freq=0.23  3 rd Passband freq=0.15  3 rd Stopband freq=0.25 

Comparison (2/14) Filter coefficient M=65 Interpolation filter by Kaiser Window Upsample=5 Cutoff freq=0.2  1 st Passband freq=0.1  1 st Stopband freq=0.3  2 nd Passband freq=0.17  2 nd Stopband freq=0.23  3 rd Passband freq=0.15  3 rd Stopband freq=0.25 

Comparison (3/14) Filter coefficient M=65 Interpolation filter by LSE FIR filter,Kaiser window and traditional Upsample=5 Cutoff freq=0.2  Passband freq=0.15  Stopband freq=0.25  Kaiser Window 1 st Passband freq=0.15  1 st Stopband freq=0.25  2 nd Passband freq=0.1  2 nd Stopband freq=0.3  3 rd Passband freq=0.17  3 rd Stopband freq=0.23 

Comparison (4/14) Filter coefficient M=65 Interpolation filter by LSE FIR filter,Kaiser window and traditional Upsample=5 Cutoff freq=0.2  Passband freq=0.15  Stopband freq=0.25  Kaiser Window 1 st Passband freq=0.15  1 st Stopband freq=0.25  2 nd Passband freq=0.1  2 nd Stopband freq=0.3  3 rd Passband freq=0.17  3 rd Stopband freq=0.23 

Comparison (5/14) Filter coefficient M=13 Interpolation filter by Kaiser window Upsample=5 Cutoff freq=0.2  Passband freq=0.17  Stopband freq=0.23   =0.06  Delta=0.016662

Comparison (6/14) Filter coefficient M=13 Interpolation filter by Kaiser window Upsample=5 Cutoff freq=0.2  Passband freq=0.17  Stopband freq=0.23   =0.06  Delta=0.016662

Comparison (7/14) Filter coefficient M=13 Interpolation filter by Kaiser window Upsample=5 Cutoff freq=0.2  Passband freq=0.15  Stopband freq=0.25   =0.1  Delta=0.002

Comparison (8/14) Filter coefficient M=13 Interpolation filter by Kaiser window Upsample=5 Cutoff freq=0.2  Passband freq=0.15  Stopband freq=0.25   =0.1  Delta=0.002

Comparison (9/14) Filter coefficient M=13 Interpolation filter by Kaiser window Upsample=5 Cutoff freq=0.2  Passband freq=0.1  Stopband freq=0.3   =0.2  Delta=1.0133*10 -5

Comparison (10/14) Filter coefficient M=13 Interpolation filter by Kaiser window Upsample=5 Cutoff freq=0.2  Passband freq=0.1  Stopband freq=0.3   =0.2  Delta=1.0133  10 -5

Comparison (11/14) Filter coefficient M=13 Ideal Interpolation filter Upsample=5 Cutoff freq=0.2  Passband freq=0.15  Stopband freq=0.25 

Comparison (12/14) Filter coefficient M=13 Ideal Interpolation filter Upsample=5 Cutoff freq=0.2  Passband freq=0.15  Stopband freq=0.25 

Comparison (13/14) Filter coefficient M=13 Interpolation filter by LSE FIR filter Upsample=5 Cutoff freq=0.2  Passband freq=0.15  Stopband freq=0.25 

Comparison (14/14) Filter coefficient M=13 Interpolation filter by LSE FIR filter Upsample=5 Cutoff freq=0.2  Passband freq=0.15  Stopband freq=0.25 

Comparison (7/14) Filter coefficient M=13 Interpolation filter by Kaiser window Upsample=5 Cutoff freq=0.2  Passband freq=0.15  Stopband freq=0.25   =0.1  Delta=0.002

Comparison (8/14) Filter coefficient M=13 Interpolation filter by Kaiser window Upsample=5 Cutoff freq=0.2  Passband freq=0.15  Stopband freq=0.25   =0.1  Delta=0.002

Conclusion & Future work The New Design Method is better than traditional Method in performance. Peak error is adjusted by transition-band in Kaiser Window. Compare the new design Method with MMSE 、 Polynomial Lagrange FIR interpolation filter. Is IIR Filter suitable for the new method??

Reference F.M.Gardner, ”Interpolation in digital modems-Part I :Fundamental” IEEE Trans.Commun.,vol.41 pp.502-508,Mar.1993 J.V.,F.L.,T.S.,andM.R. ”The effects of quantizing the fractional interval in interpolation filters” Heinrich Meyr,Marc Moeneclaey,Stefan A. Fechtel “Digital Communication Receivers”. New York :Wiley 1997 C. S. Burrus, A. W. Soewito and R. A. Gopnath, “Least Squared Error FIR Filter Design with Transition Bands,” IEEE Trans. Signal Processing, vol. 40, No. 6, pp.1327-1338, June 1992. Heinrich Meyr,Marc Moeneclaey,Stefan A. Fechtel “Digital Communication Receivers”. New York :Wiley 1997 Alan V. Oppenheim,Ronald W. Schafer with John R. Buck “Discrete- Time Signal Processing”.

~~~Happy Chinese New Year~~~~

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