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Compare ideal Interpolation filter and interpolation by LSE FIR filter(Final)
Advisor : Dr. Yung-AN Kao
Student: Ying Chun Chen
Kaiser Window
2 1 20
0
0
[ (1 [( ) / ] ) ], 0
[ ] ( )
0,
2
( ) represents the zeroth-order modified Bessel function of the first kind.
0.1102( 8.7)
I nn M
w n I
otherwise
where M
I
A0.4
, 50
0.5842( - 21) 0.07886( 21) ,21 50
0 , 21
20log 2.285 ( ) 8,
A
A A A
A
A M
Kaiser Window (Simulation)Filter coefficient M=65
Cutoff freq=0.2
1st Passband freq=0.15 1st Stopband freq=0.251st Delta=0.002
2nd Passband freq=0.1 2nd Stopband freq=0.3 2nd Delta=1.0133*10-5
3rd Passband freq=0.17 3rd Stopband freq=0.23 3rd Delta=0.016662
Comparison(1/14)Filter coefficient M=65
Interpolation filter by Kaiser Window
Upsample=5
Cutoff freq=0.2
1st Passband freq=0.1 1st Stopband freq=0.3 2nd Passband freq=0.17 2nd Stopband freq=0.23 3rd Passband freq=0.15 3rd Stopband freq=0.25
Comparison (2/14)Filter coefficient M=65
Interpolation filter by Kaiser Window
Upsample=5
Cutoff freq=0.2
1st Passband freq=0.1 1st Stopband freq=0.3 2nd Passband freq=0.17 2nd Stopband freq=0.23 3rd Passband freq=0.15 3rd 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 1st Passband freq=0.15 1st Stopband freq=0.252nd Passband freq=0.1 2nd Stopband freq=0.3 3rd Passband freq=0.17 3rd 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 1st Passband freq=0.151st Stopband freq=0.252nd Passband freq=0.12nd Stopband freq=0.3 3rd Passband freq=0.173rd 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=1.013310-5
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”.