Google scholar arxiv informatics ads IJAIS publications are indexed with Google Scholar, NASA ADS, Informatics et. al.

Call for Paper

-

March Edition 2022
International Journal of Applied Information Systems solicits high quality original research papers for the March 2022 Edition of the journal. The last date of research paper submission is February 15, 2022.

FIR Linear Phase Fractional Order Digital Differentiator Design using Convex Optimization

Simranjot Singh, Kulbir Singh Published in Signal Processing

FIR Linear Phase Fractional Order Digital Differentiator Design using Convex Optimization
International Journal of Applied Information Systems
Year of Publication: 2014
© 2013 by IJAIS Journal
Series Volume 8 Number 1
Authors Simranjot Singh, Kulbir Singh
10.5120/ijais14-451280
Download full text

  1. Simranjot Singh and Kulbir Singh. Article: FIR Linear Phase Fractional Order Digital Differentiator Design using Convex Optimization. International Journal of Applied Information Systems 8(1):29-38, December 2014. BibTeX

    @article{key:article,
	author = "Simranjot Singh and Kulbir Singh",
	title = "Article: FIR Linear Phase Fractional Order Digital Differentiator Design using Convex Optimization",
	journal = "International Journal of Applied Information Systems",
	year = 2014,
	volume = 8,
	number = 1,
	pages = "29-38",
	month = "December",
	note = "Published by Foundation of Computer Science, New York, USA"
}

Abstract

In this paper, design of linear phase FIR digital differentiators is investigated using convex optimization. The problem of differentiator design is first described in terms of convex optimization with different optimization variables' options, taken one at a time. The method is then used to design first order low pass differentiators and results are compared with Salesnick's technique and Parks McClellan algorithm. The designed FIR low pass differentiator has improvement in transition width and flexibility to optimize different parameters. The concept of low pass differentiation is further generalized to fractional order differentiators. Fractional order differentiators are designed by using minmax technique on mean square error. Design examples demonstrate easy design procedure and flexibility in the process as well as improvement over existing fractional order differentiators in terms of mean square error in passband. Finally, fractional order differentiators are designed and used for texture enhancement of color images. Better texture enhancement than existing filtering approaches is established based on average gradient and entropy values.

Reference

  1. Parks, T. W. and Burrus, C. S. 1987. Digital Filter Design. Wiley. New York.
  2. Oppenheim, A. V. and Schafer, R. W. 1999. Discrete-Time Signal Processing. Prentice-Hall, Englewood Cliffs.
  3. Davidson, T. N. 2010. Enriching the art of FIR filter design via Convex Optimization. IEEE Signal Processing Magazine.
  4. Roy, S. C. D. and Kumar, B. 1993. Handbook of Statistics. Vol. 10. Elsevier Science Publishers. Amsterdam. pp. 159-205.
  5. Tseng, C. C. and Lee, S. L. 2006. Linear phase FIR differentiator design based on maximum signal-to-noise ratio criterion. Signal Processing. vol. 86.
  6. Salesnick, I. 2002. Maximally flat lowpass digital differentiators. IEEE Trans. Circuits Syst. II. vol. 49. no. 3. pp. 219–223.
  7. Tseng, C. C. and Lee, S. L. . 2008. Design of Fractional Order Digital Differentiator Using Radial Basis Function. IEEE Transactions On Circuits And Systems—I: Regular Papers. Vol. 57. No. 7
  8. Grant, M. , Boyd S. : Graph implementations for nonsmooth convex programs. Recent Advances in Learning and Control, V. Blondel, S. Boyd, and H. Kimura, Eds. New York: Springer, pp. 95–110 [Online]. Available: http://stanford. edu/ ˜boyd/cvx (2008)
  9. Sturm, J. F. 1999. 1999. Using SeDuMi 1. 02, a Matlab toolbox for optimization over symmetric cones. Optim. Methods and Software vol. 11–12. pp. 625–653. [Online] Available: http://sedumi. ie. lehigh. edu
  10. Vanderbei, R. J. 1996. Linear Programming: Foundations and Extensions. Kluwerk. Boston
  11. Wu, S. P. , Boyd, S. , and Vandenberghe, L. 1999. FIR filter design via spectral factorization and convex optimization. Applied and Computational Control, Signals, and Circuits. vol. 1. ch. 5. pp. 215–245. Birkhauser, Cambridge, MA.
  12. Al-Alaoui, M. A. 2007. Linear phase low-pass IIR digital differentiators. IEEE Trans. Signal Process. vol. 55. no. 2. pp. 691–706
  13. Ferdi, Y. 2010. Improved Lowpass Differentiator for Physiological Signal Processing. CSNDSP 2010,. pp. 747 – 750
  14. Boyd, S. and Vandenberghe L. 2004. Convex Optimization. Cambridge Univ. Press, Cambridge. U. K.
  15. Zhao, H. , Qiu G. , Yao L. and Yu, J. . 2005. Design of fractional order digital FIR differentiators using frequency response approximation. Proc. 2005 Int. Conf. Communications, Circuits and Systems. pp. 1318–1321.
  16. Yakhdani, M. F. and Azizi, A. 2010. Quality Assessment of Image Fusion Techniques For Multisensor High Resolution Satellite Images. The International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. 38. Part 7B. pp. 204-209
  17. Hao, M. and Sun, X. . A modified Retinex Algorithm based on Wavelet Transformation. Second International Conference on MultiMedia and Information Technology 2010. pp. 306-309
  18. Garg, V. and Singh, K. . 2012. An Improved Grunwald-Letnikov Fractional Differential Mask for Image Texture Enhancement, International Journal of Advanced Computer Science and Applications. vol. 3. no. 3.
  19. Levin A. , Lischinski D. and Weiss, Y. 2008 . A closed-form solution to natural image matting. IEEE Trans. PAMI. vol. 30. pp. 228–242

Keywords

FIR Filter, Fractional order differentiator, Low pass differentiator, Full band differentiator, Image Texture Enhancement.