Efficient Design and Implementation of Variable Fractional Delay Filters Using Differentiators

In this paper, the power series expansion of exponential function is used to transform the design problem of variable fractional delay (VFD) filter into the designs of digital differentiators with various orders such that conventional digital differentiators can be applied to implement VFD filter efficiently. The proposed method is flexible because the VFD filter can be designed by making the trade-off among the storage requirement of filter coefficients, computational complexity and delay of filter. Finally, some numerical examples are demonstrated to show the effectiveness and flexibility of the proposed design methods.

[1]  Tian-Bo Deng,et al.  Symmetric Structures for Odd-Order Maximally Flat and Weighted-Least-Squares Variable Fractional-Delay Filters , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Soo-Chang Pei,et al.  Minimax Design of Variable Fractional-Delay FIR Digital Filters by Iterative Weighted Least-Squares Approach , 2008, IEEE Signal Processing Letters.

[3]  Unto K. Laine,et al.  Splitting the Unit Delay - Tools for fractional delay filter design , 1996 .

[4]  Yong Lian,et al.  Weighted-Least-Squares Design of Variable Fractional-Delay FIR Filters Using Coefficient Symmetry , 2006, IEEE Transactions on Signal Processing.

[5]  Tian-Bo Deng Robust Structure Transformation for Causal Lagrange-Type Variable Fractional-Delay Filters , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  Unto K. Laine,et al.  Splitting the unit delay [FIR/all pass filters design] , 1996, IEEE Signal Process. Mag..

[7]  Chien-Cheng Tseng,et al.  An efficient design of a variable fractional delay filter using a first-order differentiator , 2003, IEEE Signal Process. Lett..

[8]  Wu-Sheng Lu,et al.  An improved weighted least-squares design for variable fractional delay FIR filters , 1999 .

[9]  H. Johansson,et al.  On the design of adjustable fractional delay FIR filters using digital differentiators , 2003, The 2010 International Conference on Green Circuits and Systems.

[10]  Tian-Bo Deng Noniterative WLS design of allpass variable fractional-delay digital filters , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  E. Hermanowicz,et al.  On designing minimax adjustable wideband fractional delay FIR filters using two-rate approach , 2005, Proceedings of the 2005 European Conference on Circuit Theory and Design, 2005..

[12]  Soo-Chang Pei,et al.  An efficient design of a variable fractional delay filter using a first-order differentiator , 2003, IEEE Signal Processing Letters.

[13]  Chien-Cheng Tseng,et al.  A comb filter design using fractional-sample delay , 1997, Proceedings of 1997 IEEE International Symposium on Circuits and Systems. Circuits and Systems in the Information Age ISCAS '97.

[14]  Chien-Cheng Tseng,et al.  Design of 1-D and 2-D variable fractional delay allpass filters using weighted least-squares method , 2002 .

[15]  T. Saramaki,et al.  Multiplication-Free Polynomial-Based FIR Filters with an Adjustable Fractional Delay , 2006 .

[16]  Jorge Herbert de Lira,et al.  Two-Dimensional Signal and Image Processing , 1989 .

[17]  Soo-Chang Pei,et al.  A generalized approach to the design of variable fractional-delay FIR digital filters , 2008, Signal Process..

[18]  Tian-Bo Deng Minimax Design of Low-Complexity Allpass Variable Fractional-Delay Digital Filters , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  Soo-Chang Pei,et al.  A New Criterion for the Design of Variable Fractional-Delay FIR Digital Filters , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  M. Skolnik,et al.  Introduction to Radar Systems , 2021, Advances in Adaptive Radar Detection and Range Estimation.

[21]  Soo-Chang Pei,et al.  WLS Design of Variable Fractional-Delay FIR Filters Using Coefficient Relationship , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[22]  Soo-Chang Pei,et al.  Two-Dimensional Farrow Structure and the Design of Variable Fractional-Delay 2-D FIR Digital Filters , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[23]  Chien-Cheng Tseng,et al.  Closed-form design of variable fractional delay filter using discrete Fourier transform , 2009, 2009 17th European Signal Processing Conference.

[24]  Tian-Bo Deng Non-iterative WLS design of allpass variable fractional-delay digital filters , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[25]  Tian-Bo Deng Coefficient-Symmetries for Implementing Arbitrary-Order Lagrange-Type Variable Fractional-Delay Digital Filters , 2007, IEEE Transactions on Signal Processing.

[26]  Eduardo A. B. da Silva,et al.  Digital Signal Processing: System Analysis and Design , 2002 .

[27]  Tian-Bo Deng,et al.  Hybrid Structures for Low-Complexity Variable Fractional-Delay FIR Filters , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  Chien-Cheng Tseng,et al.  Design of variable fractional delay FIR filter using differentiator bank , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[29]  Peng-Hua Wang,et al.  Closed-form design of maximally flat FIR fractional delay filters using interlaced sampling method , 2013, SiPS 2013 Proceedings.

[30]  Chien-Cheng Tseng,et al.  Design of digital differentiator using difference formula and Richardson extrapolation , 2008 .