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

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”.

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