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MMSE FIR Interpolation Filter. Advisor : Dr. Yung-AN Kao Student: Ying Chun Chen. Reference. Heinrich Meyr, Marc Moeneclaey, and Stefan A. Fechtel Digital Communication Receivers , John Wiley& Sons, LTD, 1997. Outlines. Introduce to MMSE Simulation - PowerPoint PPT Presentation
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MMSE FIR Interpolation Filter
Advisor : Dr. Yung-AN Kao
Student: Ying Chun Chen
Reference
• Heinrich Meyr, Marc Moeneclaey, and Stefan A. Fechtel Digital Communication Receivers, John Wiley& Sons, LTD, 1997
Outlines
• Introduce to MMSE
• Simulation
• Compare with Interpolation filter based on upsampling
• Conclusion
Introduce to MMSE FIR Interpolation filter
Error function as follow (1)
where B is the one-sided signal bandwidth
I1=N and I2=N-1
From this it follows that the number of samples should be even
2
1
222
2
( ) ( ) min . (1)s s
B Ij T j T n
nn IB
e e h e d
Introduce to MMSE FIR Interpolation filter
To obtain the minimum
(2)
(3)
R = RH (4)
R is Toeplitz matrix
( )0
( )m
e
h
2 21( ) ( )
2 2
( )s s
B BNj T m j T n m
nn NB B
e d h e d
Simulation
n \ 0.1 0.2 0.3 0.4 0.5-4 -0.001959 -0.0037645 -0.0052573 -0.006298 -0.0067775
-3 0.010908 0.021177 0.029895 0.036224 0.039458
-2 -0.03599 -0.07127 -0.10281 -0.12758 -0.14266
-1 0.10792 0.22795 0.35522 0.48438 0.60984
0 0.96819 0.90965 0.82755 0.726 0.60984
1 -0.061569 -0.10614 -0.13381 -0.14545 -0.14266
2 0.014814 0.026616 0.034802 0.039078 0.039458
3 -0.0024026 -0.0043859 -0.00582 -0.0066262 -0.0067775
Frequency Response
Interpolation filter by LSE
Passband 0.15
Stopband 0.25
Interpolation filter coefficient length 10
Cutoff frequency 0.2
MMSE Interpolation filter
B=0.375
N=5
Delay information =0.4
Frequency Response
Interpolation filter by LSE
Passband 0.15
Stopband 0.25
Interpolation filter coefficient length 10
Cutoff frequency 0.2
MMSE Interpolation filter
B=0.375
N=5
Delay information =0.4
Error Performance
Interpolation filter by LSE
Passband 0.15
Stopband 0.25
Interpolation filter coefficient length 10
Cutoff frequency 0.2
MMSE Interpolation filter
B=0.375
N=5
Delay information =0.4
Group Delay
Interpolation filter by LSE
Passband 0.15
Stopband 0.25
Interpolation filter coefficient length 10
Cutoff frequency 0.2
MMSE Interpolation filter
B=0.375
N=5
Delay information =0.4
Conclusion
• The MMSE interpolation filter has larger error than interpolation filter by LSE in frequency domain and error performance
• Complexity of Computation in MMSE interpolation filter is the same as interpolation filter by LSE.