MMSE FIR Interpolation Filter

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

Error Performance


Passband 0.15

Stopband 0.25




B=0.375

N=5


Group Delay


Passband 0.15

Stopband 0.25




B=0.375

N=5


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.

MMSE FIR Interpolation Filter

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