American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Auction games for coordination of large-scale elastic loads in deregulated electricity markets
  • JIMO Home
  • This Issue
  • Next Article
    An improved approximation scheme for scheduling a maintenance and proportional deteriorating jobs
July  2016, 12(3): 819-831. doi: 10.3934/jimo.2016.12.819

Variable fractional delay filter design with discrete coefficients

Hai Huyen Dam 1, and  Kok Lay Teo 1,

1. 

Dept. of Mathematics and Statistics, Curtin University of Technology, Perth, Australia, Australia

Received  May 2014 Revised  June 2014 Published  September 2015

This paper investigates the optimal design of variable fractional delay (VFD) filter with discrete coefficients as a means of achieving low complexity and efficient hardware implementation. The filter coefficients are expressed as the sum of signed power-of-two (SPT) terms with a restriction on the total number of power-of-two terms. An optimization problem with least squares criterion is formulated as a mixed-integer programming problem. An optimal scaling factor quantization scheme is applied to the problem resulting in an optimal scaling factor quantized solution. This solution is then improved further by applying a discrete filled function, that has been extended for a mixed integer optimization problem. To apply the discrete filled function method, it requires multiple calculations of the objective function around the neighborhood of a searched point. Thus, an updating scheme is developed to efficiently calculate the objective function in a neighborhood of a point. Design examples demonstrate the effectiveness of the proposed optimization approach.
Keywords: discrete filled function, Variable fractional delay, signed power-of-two (SPT) coefficients..
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Hai Huyen Dam, Kok Lay Teo. Variable fractional delay filter design with discrete coefficients. Journal of Industrial & Management Optimization, 2016, 12 (3) : 819-831. doi: 10.3934/jimo.2016.12.819
References:
[1]

H. H. Dam, A. Cantoni, K. L. Teo and S. Nordholm, Variable digital filter with least square criterion and peak gain constraints,, IEEE Trans. Circuits Systems II, 54 (2007), 24.   Google Scholar

[2]

H. H. Dam, A. Cantoni, K. L. Teo and S. Nordholm, Variable digital filter with group delay flatness specification or phase constraints,, IEEE Trans. Circuits Systems II, 55 (2008), 442.   Google Scholar

[3]

H. H. Dam, A. Cantoni, K. L. Teo and S. Nordholm, FIR variable digital filter with signed power-of-two coefficients,, IEEE Trans. Circuits Systems I, 54 (2007), 1348.  doi: 10.1109/TCSI.2007.897775.  Google Scholar

[4]

H. H. Dam, Design of allpass variable fractional delay filter with powers-of-two coefficients,, IEEE Signal Processing Letters, 22 (2015), 1643.  doi: 10.1109/LSP.2015.2420652.  Google Scholar

[5]

H. H. Dam, Design of variable fractional delay filter with fractional delay constraints,, IEEE Signal Processing Letters, 21 (2014), 1361.  doi: 10.1109/LSP.2014.2336662.  Google Scholar

[6]

H. H. Dam and K. L. Teo, Allpass VFD filter design,, IEEE Trans. Signal Processing, 58 (2010), 4432.  doi: 10.1109/TSP.2010.2048316.  Google Scholar

[7]

H. H. Dam, Variable Fractional Delay Filter with Sub-Expressions Coefficients,, International Journal of Innovative Computing, 9 (2013), 2995.   Google Scholar

[8]

T.-B. Deng and S. Chivapreecha, Bi-minimax design of even-order variable fractional-delay FIR digital filters,, IEEE Trans. Circuits Systems I: Reg. Paper, 59 (2012), 1766.  doi: 10.1109/TCSI.2011.2180431.  Google Scholar

[9]

T.-B. Deng and W. Qin, Coefficient relation-based minimax design and low-complexity structure of variable fractional-delay digital filters,, Signal Processing, 93 (2013), 923.  doi: 10.1016/j.sigpro.2012.11.004.  Google Scholar

[10]

T.-B. Deng, Decoupling minimax design of low-complexity variable fractional-delay FIR digital filters,, IEEE Trans. Circuits Syst. I: Reg. Papers, 58 (2011), 2398.  doi: 10.1109/TCSI.2011.2123510.  Google Scholar

[11]

C. W. Farrow, A continuously variable digital delay element,, in Proc. IEEE Int. Symp. Circuits Syst., (1988), 2641.  doi: 10.1109/ISCAS.1988.15483.  Google Scholar

[12]

Y.-D. Huang, S.-C. Pei and J.-J. Shyu, WLS design of variable fractional-delay FIR filters using coefficient relationship,, IEEE Trans. Circuits Systems II: Express Brief, 56 (2009), 220.   Google Scholar

[13]

D. Li, Y. C. Lim and Y. Lian, A polynomial-time algorithm for designing FIR filters with power-of-two coefficients,, IEEE Trans. Signal Processing, 50 (2002), 1935.   Google Scholar

[14]

Y. C. Lim, Design of discrete-coefficient-value linear phase FIR filters with optimum normalized peak ripple magnitude,, in IEEE Trans. Circuits Systems, 37 (1990), 1480.  doi: 10.1109/31.101268.  Google Scholar

[15]

H. Lin, Y. Wang and X. Wang, An auxiliary function method for global minimization in integer programming,, Mathematical Problems in Engineering, 2011 (2011), 1.  doi: 10.1155/2011/402437.  Google Scholar

[16]

C. K. S. Pun, Y. C. Wu, S. C. Chan and K. L. Ho, On the design and efficient implementation of the Farrow structure,, IEEE Signal Processing Letters, 10 (2003), 189.  doi: 10.1109/LSP.2003.813681.  Google Scholar

show all references

References:
[1]

H. H. Dam, A. Cantoni, K. L. Teo and S. Nordholm, Variable digital filter with least square criterion and peak gain constraints,, IEEE Trans. Circuits Systems II, 54 (2007), 24.   Google Scholar

[2]

H. H. Dam, A. Cantoni, K. L. Teo and S. Nordholm, Variable digital filter with group delay flatness specification or phase constraints,, IEEE Trans. Circuits Systems II, 55 (2008), 442.   Google Scholar

[3]

H. H. Dam, A. Cantoni, K. L. Teo and S. Nordholm, FIR variable digital filter with signed power-of-two coefficients,, IEEE Trans. Circuits Systems I, 54 (2007), 1348.  doi: 10.1109/TCSI.2007.897775.  Google Scholar

[4]

H. H. Dam, Design of allpass variable fractional delay filter with powers-of-two coefficients,, IEEE Signal Processing Letters, 22 (2015), 1643.  doi: 10.1109/LSP.2015.2420652.  Google Scholar

[5]

H. H. Dam, Design of variable fractional delay filter with fractional delay constraints,, IEEE Signal Processing Letters, 21 (2014), 1361.  doi: 10.1109/LSP.2014.2336662.  Google Scholar

[6]

H. H. Dam and K. L. Teo, Allpass VFD filter design,, IEEE Trans. Signal Processing, 58 (2010), 4432.  doi: 10.1109/TSP.2010.2048316.  Google Scholar

[7]

H. H. Dam, Variable Fractional Delay Filter with Sub-Expressions Coefficients,, International Journal of Innovative Computing, 9 (2013), 2995.   Google Scholar

[8]

T.-B. Deng and S. Chivapreecha, Bi-minimax design of even-order variable fractional-delay FIR digital filters,, IEEE Trans. Circuits Systems I: Reg. Paper, 59 (2012), 1766.  doi: 10.1109/TCSI.2011.2180431.  Google Scholar

[9]

T.-B. Deng and W. Qin, Coefficient relation-based minimax design and low-complexity structure of variable fractional-delay digital filters,, Signal Processing, 93 (2013), 923.  doi: 10.1016/j.sigpro.2012.11.004.  Google Scholar

[10]

T.-B. Deng, Decoupling minimax design of low-complexity variable fractional-delay FIR digital filters,, IEEE Trans. Circuits Syst. I: Reg. Papers, 58 (2011), 2398.  doi: 10.1109/TCSI.2011.2123510.  Google Scholar

[11]

C. W. Farrow, A continuously variable digital delay element,, in Proc. IEEE Int. Symp. Circuits Syst., (1988), 2641.  doi: 10.1109/ISCAS.1988.15483.  Google Scholar

[12]

Y.-D. Huang, S.-C. Pei and J.-J. Shyu, WLS design of variable fractional-delay FIR filters using coefficient relationship,, IEEE Trans. Circuits Systems II: Express Brief, 56 (2009), 220.   Google Scholar

[13]

D. Li, Y. C. Lim and Y. Lian, A polynomial-time algorithm for designing FIR filters with power-of-two coefficients,, IEEE Trans. Signal Processing, 50 (2002), 1935.   Google Scholar

[14]

Y. C. Lim, Design of discrete-coefficient-value linear phase FIR filters with optimum normalized peak ripple magnitude,, in IEEE Trans. Circuits Systems, 37 (1990), 1480.  doi: 10.1109/31.101268.  Google Scholar

[15]

H. Lin, Y. Wang and X. Wang, An auxiliary function method for global minimization in integer programming,, Mathematical Problems in Engineering, 2011 (2011), 1.  doi: 10.1155/2011/402437.  Google Scholar

[16]

C. K. S. Pun, Y. C. Wu, S. C. Chan and K. L. Ho, On the design and efficient implementation of the Farrow structure,, IEEE Signal Processing Letters, 10 (2003), 189.  doi: 10.1109/LSP.2003.813681.  Google Scholar

[1]

Bin Li, Hai Huyen Dam, Antonio Cantoni. A global optimal zero-forcing Beamformer design with signed power-of-two coefficients. Journal of Industrial & Management Optimization, 2016, 12 (2) : 595-607. doi: 10.3934/jimo.2016.12.595
[2]

Jamel Ben Amara, Emna Beldi. Simultaneous controllability of two vibrating strings with variable coefficients. Evolution Equations & Control Theory, 2019, 8 (4) : 687-694. doi: 10.3934/eect.2019032
[3]

Yongjian Yang, Zhiyou Wu, Fusheng Bai. A filled function method for constrained nonlinear integer programming. Journal of Industrial & Management Optimization, 2008, 4 (2) : 353-362. doi: 10.3934/jimo.2008.4.353
[4]

Liuyang Yuan, Zhongping Wan, Jingjing Zhang, Bin Sun. A filled function method for solving nonlinear complementarity problem. Journal of Industrial & Management Optimization, 2009, 5 (4) : 911-928. doi: 10.3934/jimo.2009.5.911
[5]

Mahmoud Abouagwa, Ji Li. G-neutral stochastic differential equations with variable delay and non-Lipschitz coefficients. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1583-1606. doi: 10.3934/dcdsb.2019241
[6]

Hasib Khan, Cemil Tunc, Aziz Khan. Green function's properties and existence theorems for nonlinear singular-delay-fractional differential equations. Discrete & Continuous Dynamical Systems - S, 2020, 13 (9) : 2475-2487. doi: 10.3934/dcdss.2020139
[7]

Antonio Coronel-Escamilla, José Francisco Gómez-Aguilar. A novel predictor-corrector scheme for solving variable-order fractional delay differential equations involving operators with Mittag-Leffler kernel. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 561-574. doi: 10.3934/dcdss.2020031
[8]

Jamel Ben Amara, Hedi Bouzidi. Exact boundary controllability for the Boussinesq equation with variable coefficients. Evolution Equations & Control Theory, 2018, 7 (3) : 403-415. doi: 10.3934/eect.2018020
[9]

Fágner D. Araruna, Flank D. M. Bezerra, Milton L. Oliveira. Rate of attraction for a semilinear thermoelastic system with variable coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3211-3226. doi: 10.3934/dcdsb.2018316
[10]

Kateřina Škardová, Tomáš Oberhuber, Jaroslav Tintěra, Radomír Chabiniok. Signed-distance function based non-rigid registration of image series with varying image intensity. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020386
[11]

Jongkeun Choi, Ki-Ahm Lee. The Green function for the Stokes system with measurable coefficients. Communications on Pure & Applied Analysis, 2017, 16 (6) : 1989-2022. doi: 10.3934/cpaa.2017098
[12]

Nguyen Huy Tuan, Tran Ngoc Thach, Yong Zhou. On a backward problem for two-dimensional time fractional wave equation with discrete random data. Evolution Equations & Control Theory, 2020, 9 (2) : 561-579. doi: 10.3934/eect.2020024
[13]

Haixia Yu. Hilbert transforms along double variable fractional monomials. Communications on Pure & Applied Analysis, 2019, 18 (3) : 1433-1446. doi: 10.3934/cpaa.2019069
[14]

Dina Tavares, Ricardo Almeida, Delfim F. M. Torres. Fractional Herglotz variational problems of variable order. Discrete & Continuous Dynamical Systems - S, 2018, 11 (1) : 143-154. doi: 10.3934/dcdss.2018009
[15]

Vo Van Au, Mokhtar Kirane, Nguyen Huy Tuan. Determination of initial data for a reaction-diffusion system with variable coefficients. Discrete & Continuous Dynamical Systems - A, 2019, 39 (2) : 771-801. doi: 10.3934/dcds.2019032
[16]

Stephanie Flores, Elijah Hight, Everardo Olivares-Vargas, Tamer Oraby, Jose Palacio, Erwin Suazo, Jasang Yoon. Exact and numerical solution of stochastic Burgers equations with variable coefficients. Discrete & Continuous Dynamical Systems - S, 2020, 13 (10) : 2735-2750. doi: 10.3934/dcdss.2020224
[17]

Shikuan Mao, Yongqin Liu. Decay property for solutions to plate type equations with variable coefficients. Kinetic & Related Models, 2017, 10 (3) : 785-797. doi: 10.3934/krm.2017031
[18]

Takahiro Hashimoto. Nonexistence of weak solutions of quasilinear elliptic equations with variable coefficients. Conference Publications, 2009, 2009 (Special) : 349-358. doi: 10.3934/proc.2009.2009.349
[19]

M. Eller, Roberto Triggiani. Exact/approximate controllability of thermoelastic plates with variable thermal coefficients. Discrete & Continuous Dynamical Systems - A, 2001, 7 (2) : 283-302. doi: 10.3934/dcds.2001.7.283
[20]

Bei Gong, Zhen-Hu Ning, Fengyan Yang. Stabilization of the transmission wave/plate equation with variable coefficients on $ {\mathbb{R}}^n $. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020068

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (23)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences