A Frequency-Domain Approach to polynomial-Based Interpolation and the Farrow Structure Advisor : Yung-An Kao Student : Chih-Wei Chen 2006/3/24

 Jussi Vesma  IEEE TRANSACTION ON CIRCUITS AND SYSTEMS- II:ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 47, NO. 3, MARCH 2000

Outline  Introduction  Efficient implementation-the Farrow structure  The frequency-domain approach  Simulation  Conclusion

Introduction  Frequency-domain relationship between the Farrow structure and the hybrid A/D model is derived.  The polynomial-based interpolation filters which can be efficiently implemented using the Farrow structure.  The advantage of the hybrid A/D system is that it is independent of the fractional interval.  This result can be utilized to develop efficient design algorithms for polynomial-based interpolation filters.

Introduction

Farrow structure  Farrow structure consists L+1 parallel FIR filter, the transfer functions  If basis function (2  -1) L:degree C(n):coefficient

Farrow structure

The frequency-domain approach  The transfer function of this discrete time filter  Rewrite

The frequency-domain approach  Set discrete time frequency response  The frequency response of anti-imaging filter

The frequency-domain approach  Avoid aliasing (not band limited)  After some manipulations

The frequency-domain approach  Finally

Simulation Minimax synthesis technique L=3 N=8 Ps=0.35Fs Ws=0.65Fs Weight=1:4

Conclusion  This result can be used to analyze the performance of different polynomial-based interpolation filters or to optimize the coefficients of the Farrow structure in the frequency domain  Utilize the result, to develop efficient design algorithm for polynomial-based interpolation filters.