Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30184
Design of Variable Fractional-Delay FIR Differentiators

Authors: Jong-Jy Shyu, Soo-Chang Pei, Min-Han Chang

Abstract:

In this paper, the least-squares design of variable fractional-delay (VFD) finite impulse response (FIR) digital differentiators is proposed. The used transfer function is formulated so that Farrow structure can be applied to realize the designed system. Also, the symmetric characteristics of filter coefficients are derived, which leads to the complexity reduction by saving almost a half of the number of coefficients. Moreover, all the elements of related vectors or matrices for the optimal process can be represented in closed forms, which make the design easier. Design example is also presented to illustrate the effectiveness of the proposed method.

Keywords: Differentiator, variable fractional-delay filter, FIR filter, least-squares method, Farrow structure.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070077

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1041

References:


[1] S. Usui and I. Amidror, "Digital low-pass differentiation for biological signal processing,-- IEEE Trans. Biomed. Eng., vol.BME-29, no.10, pp.686-693, Oct. 1982.
[2] R. C. Kavanagh, "FIR differentiators for quantized signals,-- IEEE Trans. Signal Process., vol.49, no.11, pp.2713-2720, Nov. 2001.
[3] J. Luo, J. Bai, P. He and K. Ying, "Axial strain calculation using a low-pass digital differentiator in ultrasound elastography,-- IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol.51, no.9, pp.1119-1127, Sep. 2004.
[4] S. L. Lin and S. Mourad, "On-chip rise-time measurement,-- IEEE Trans. Instrum. Meas., vol.53, no.6, pp.1510-1516, Dec. 2004.
[5] S.-C. Pei and J.-J. Shyu, "Eigenfilter design of high-order digital differentiators,-- IEEE Trans. Acoust., Speech, Signal Process., vol.37, no.4, pp.505-511, Apr. 1989.
[6] S. Sunder, Y. Su, A. Antoniou and W.-S. Lu , "Design of digital differentiators satisfying prescribed specifications using optimization techniques,-- in Proc. ISCAS 1989, May 1989, pp.1652-1655.
[7] B. Kumar, S. C. D. Roy and H. Shah, "On the design of FIR digital differentiators which are maximally linear at the frequency ¶Çüô / p , p¶ÇéŶÇü×positive integers¶Çüá ,-- IEEE Trans. Signal Process., vol.40, no.9, pp.2334-2338, Sep. 1992.
[8] E. Hermanowicz and M. Rojewski, "Design of FIR first order digital differentiators of variable fractional sample delay using maximally flat error criterion,-- Electron. Lett., vol.30, no.1, pp.17-18, Jan. 1994.
[9] M. A. Al-Alaoui, "Novel IIR differentiator from the Simpon integration rule,-- IEEE Trans. Circuits Syst. I, Fundament. Theory Appl., vol.41, no.2, pp.186-187, Feb. 1994.
[10] X. Zhang and T. Yoshikawa, "Design of full band IIR digital differentiators,-- in Proc. IEEE Int. Conf. Neural Net. Signal Process., Dec. 2003, pp.652-655.
[11] C.-C. Tseng, "Digital differentiator design using fractional delay filter and limit computation,-- IEEE Trans. Circuits Syst. I, Reg. Papers, vol.52, no.10, pp.2248-2259, Oct. 2005.
[12] N. Q. Ngo, "A new approach for the design of wideband digital integrator and differentiator,-- IEEE Trans. Circuits Syst. II, Exp. Briefs, vol.53, no.9, pp.936-940, Sep. 2006.
[13] M. A. Al-Alaoui, "Linear phase low-pass IIR digital differentiators,-- IEEE Trans. Signal Process., vol.55, no.2, pp.697-706, Feb. 2007.
[14] C.-C. Tseng and S.-L. Lee, "Design of digital differentiator using difference formula and Richardson extrapolation,-- vol.2, no.2, pp.177-188, Jun. 2008.
[15] C. Y.-F. Ho, B. W.-K. Ling, Y.-Q. Liu, P. K.-S. Tam and K.-L. Teo, "Optimum design of discrete-time differentiators via semi-infinite programming approach,-- IEEE Trans. Instrum. Meas., vol.57, no.10, pp.2226-2230, Oct. 2008.
[16] C. W. Farrow, "A continuously variable digital delay element,-- in Proc. ISCAS 1988, May 1988, pp.2641-2645.
[17] T. I. Laakso, V. Välimäki, M. Karjalainen and U. K. Laine, "Splitting the unit delay: Tools for fractional delay filter design,-- IEEE Signal Process. Mag., vol.13, pp.30-60, Jan. 1996.
[18] W.-S. Lu and T.-B. Deng, "An improved weighted least-squares design for variable fractional delay FIR filters,-- IEEE Trans. Circuits Syst. I, Analog Digit. Signal Process., vol.46, no.8, pp.1035-1040, Aug. 1999.
[19] H. Johansson and P. Löwenborg, "On the design of adjustable fractional delay FIR filters,-- IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol.50, no.4, pp.164-169, Apr. 2003.
[20] C.-C. Tseng, "Design of variable fractional delay FIR filter using symmetry,-- in Proc. ISCAS 2004, May 2004, pp.III/477-III/480.
[21] H. Zhao and J. Yu, "A simple and efficient design of variable fractional delay FIR filters,-- IEEE Trans. Circuits Syst. II, Exp. Briefs, vol.53, no.2, pp.157-160, Feb. 2006.
[22] T.-B. Deng, and Y. Lian, "Weighted-least-squares design of variable fractional-delay FIR filters using coefficient symmetry,-- IEEE Trans. Signal Process., vol.54, no.8, pp.3023-3038, Aug. 2006.
[23] E. Hermanowice and H. Johansson, "A complex variable fractional-delay FIR filter structure,-- IEEE Trans. Circuits Syst. II, Exp. Briefs, vol.54, no.9, pp.785-789, Sep. 2007.
[24] T.-B. Deng, "Symmetric structures for odd-order maximally flat and weighted-least- squares variable fractional-delay filters,-- IEEE Trans. Circuits Syst. I, Reg. Papers, vol.54, no.12, pp.2718-2732, Dec. 2007
[25] C. Y. Chi and Y. T. Kou, "A new self-initiated optimum WLS approximation method for the design of linear phase FIR digital filters,-- in Proc. ISCAS 1991, June 1991, pp.168-171.