compare ideal interpolation filter and interpolation by lse fir filter(2)
DESCRIPTION
Compare ideal Interpolation filter and interpolation by LSE FIR filter(2). Advisor : Dr. Yuan-AN Kao Student: Bill Chen. Outline. FIR Filter by Windowing Comparison (Simulation) Conclusion Reference. Design of FIR Filter By Windowing(1/2). Design of FIR Filter By Windowing (1/2). - PowerPoint PPT PresentationTRANSCRIPT
Compare ideal Interpolation filter and interpolation by LSE FIR filter(2)
Advisor : Dr. Yuan-AN Kao
Student: Bill Chen
Outline
• FIR Filter by Windowing• Comparison (Simulation)
• Conclusion
• Reference
Design of FIR Filter By Windowing(1/2)
-
-
-
( ) [ ]
[ ]
1[ ] ( )
2
j j nd d
n
d
j j nd d
Ideal desired frequency response
H e h n e
h n is the corresponding impulse response sequence
h n H e e d
Design of FIR Filter By Windowing (1/2)
[ ] [ ]
[ ] ,0[ ]
0 ,
[ ]
-
define h n is to define a new system with impulse response h ndh n n Mdh n
otherwise
we can respresent h n as the product of the desired impulse
response and a finite duration
" " [ ]
[ ] [ ] [ ] , 0
1 ( - )( ) ( ) ( )-2
window w n
h n h n w n n Md
j j jH e H e W e dd
Kaiser Window & Simulation
2 1 20
0
0
[ (1 [( ) / ] ) ], 0
[ ] ( )
0,
2
( ) - mod .
0.1102( 8.7)
=
I nn M
w n I
otherwise
where M
I represents the zeroth order ified Bessel function of the first kind
A
0.4
10
,A>50
0.5842(A-21) 0.07886( 21) ,21 50
0 ,A<21
20log
A A
A
Kaiser Window (Simulation)
M+1=55
Alpha=0.5M
Beta
Kaiser Window (Simulation)
Comparison(1/14)Filter coefficient M=55
Interpolation filter by LSE FIR filter
Upsample=5
Cutoff freq=0.2pi
Passband freq=0.15pi
Stopband freq=0.25pi
Ideal interpolation filter with Kaiser Window
Alpha=0.5*(M-1)
Beta
Comparison (2/14)Filter coefficient M=55
Interpolation filter by LSE FIR filter
Upsample=5
Cutoff freq=0.2pi
Passband freq=0.15pi
Stopband freq=0.25pi
Ideal interpolation filter with Kaiser Window
Alpha=0.5*(M-1)
Beta
Comparison (3/14)Filter coefficient M=55
Interpolation filter by LSE FIR filter
Upsample=5
Cutoff freq=0.2pi
Passband freq=0.1pi
Stopband freq=0.3pi
Ideal interpolation filter with Kaiser Window
Alpha=0.5*(M-1)
Beta
Comparison (4/14)
Filter coefficient M=55
Interpolation filter by LSE FIR filter
Upsample=5
Cutoff freq=0.2pi
Passband freq=0.1pi
Stopband freq=0.3pi
Ideal interpolation filter with Kaiser Window
Alpha=0.5*(M-1)
Beta
Comparison (5/14)Filter coefficient M=55
Interpolation filter by LSE FIR filter
Upsample=5
Cutoff freq=0.2pi
Passband freq=0.17pi
Stopband freq=0.23pi
Ideal interpolation filter with Kaiser Window
Alpha=0.5*(M-1)
Beta
Comparison (6/14)Filter coefficient M=55
Interpolation filter by LSE FIR filter
Upsample=5
Cutoff freq=0.2pi
Passband freq=0.17pi
Stopband freq=0.23pi
Ideal interpolation filter with Kaiser Window
Alpha=0.5*(M-1)
Beta
Comparison (7/14)Filter coefficient M=11
Interpolation filter by LSE FIR filter
Upsample=5
Cutoff freq=0.2pi
Passband freq=0.15pi
Stopband freq=0.25pi
Ideal interpolation filter with Kaiser Window
Alpha=0.5*(M-1)
Beta0
Comparison (8/14)Filter coefficient M=11
Interpolation filter by LSE FIR filter
Upsample=5
Cutoff freq=0.2pi
Passband freq=0.15pi
Stopband freq=0.25pi
Ideal interpolation filter with Kaiser Window
Alpha=0.5*(M-1)
Beta0
Comparison (9/14)Filter coefficient M=11
Interpolation filter by LSE FIR filter
Upsample=5
Cutoff freq=0.2pi
Passband freq=0.15pi
Stopband freq=0.25pi
Ideal interpolation filter with Kaiser Window
Alpha=0.5*(M-1)
Beta3
Comparison (10/14)Filter coefficient M=11
Interpolation filter by LSE FIR filter
Upsample=5
Cutoff freq=0.2pi
Passband freq=0.15pi
Stopband freq=0.25pi
Ideal interpolation filter with Kaiser Window
Alpha=0.5*(M-1)
Beta3
Comparison (11/14)Filter coefficient M=11
Interpolation filter by LSE FIR filter
Upsample=5
Cutoff freq=0.2pi
Passband freq=0.15pi
Stopband freq=0.25pi
Ideal interpolation filter with Kaiser Window
Alpha=0.5*(M-1)
Beta6
Comparison (12/14)Filter coefficient M=11
Interpolation filter by LSE FIR filter
Upsample=5
Cutoff freq=0.2pi
Passband freq=0.15pi
Stopband freq=0.25pi
Ideal interpolation filter with Kaiser Window
Alpha=0.5*(M-1)
Beta6
Comparison (13/14)Filter coefficient M=11
Interpolation filter by LSE FIR filter
Upsample=5
Cutoff freq=0.2pi
Passband freq=0.15pi
Stopband freq=0.25pi
Comparison (14/14)Filter coefficient M=11
Interpolation filter by LSE FIR filter
Upsample=5
Cutoff freq=0.2pi
Passband freq=0.15pi
Stopband freq=0.25pi
Conclusion
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”.