Design of digital differentiator using difference formula and Richardson extrapolation

Access Full Text

Design of digital differentiator using difference formula and Richardson extrapolation

For access to this article, please select a purchase option:

Buy article PDF
£12.50
(plus tax if applicable)
Add to cart
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)
Add to cart

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Signal Processing — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

© The Institution of Engineering and Technology
Published

The design of digital differentiators is investigated. First, the backward difference formula in numerical differentiation is applied to derive the transfer function of a digital differentiator. In this design, the Richardson extrapolation is used to generate high-accuracy results while using low-order formulas. Then, conventional Lagrange finite impulse response (FIR) and Thiran infinite impulse response (IIR) allpass fractional delay filters are directly applied to implement the designed differentiator. Next, the proposed method is extended to design digital differentiators using central difference formula. Finally, several numerical examples are illustrated to demonstrate the effectiveness of this new design approach.

Inspec keywords: extrapolation; IIR filters; FIR filters; transfer functions

Other keywords: Richardson extrapolation; transfer function; infinite impulse response; allpass fractional delay filters; digital differentiator design; difference formula; Lagrange finite impulse response

Subjects: Interpolation and function approximation (numerical analysis); Digital filters; Digital filters; Interpolation and function approximation (numerical analysis)

References

    1. 1)
      • S. Sunder , V. Ramachandran . Design of equiripple nonrecursive digital differentiators and Hilbert transformers using a weighted least-squares technique. IEEE Trans. Signal Process. , 2504 - 2509
    2. 2)
      • S.C. Pei , J.J. Shyu . Eigenfilter design of higher-order digital differentiators. IEEE Trans. Acoust. Speech Signal Process. , 505 - 511
    3. 3)
      • Y.Q. Chen , K.L. Moore . Discretization schemes for fractional order differentiators and integrators. IEEE Trans. Circuits Syst. I , 363 - 367
    4. 4)
      • B.M. Vinagre , Y.Q. Chen , I. Petras . Two direct Tustin discretization methods for fractional-order differentiator/integrators. J. Franklin Inst. , 349 - 362
    5. 5)
      • C.C. Tseng . Design of fractional order digital FIR differentiators. IEEE Signal Process. Lett. , 77 - 79
    6. 6)
      • M.I. Skolnik . (2001) Introduction to radar systems.
    7. 7)
      • K. Rahul , S.N. Bhattacharyya . One-sided finite-difference approximations suitable for use with Richardson extrapolation. J. Comput. Phys. , 13 - 20
    8. 8)
      • J.H. Mathews , K.D. Fink . (2004) Numerical methods using MATLAB.
    9. 9)
      • R.L. Burden , J.D. Faires . (1993) Numerical analysis.
    10. 10)
      • D.C. Joyce . Survey of extrapolation processes in numerical analysis. SIAM Rev. , 435 - 490
    11. 11)
      • S. Usui , I. Amidror . Digital low-pass differentiation for biological signal processing. IEEE Trans. Biomed. Eng. , 686 - 693
    12. 12)
      • S. Nakamura . (2002) Numerical analysis and graphic visualization with MATLAB.
    13. 13)
      • T.I. Laakso , V. Valimaki , M. Karjalainen , U.K. Laine . Splitting the unit delay: tool for fractional delay filter design. IEEE Signal Process. Mag. , 30 - 60
    14. 14)
      • J.S. Lim . (1990) Two dimensional signal and image processing.
    15. 15)
      • Y.Q. Chen , B.M. Vinagre . A new IIR-type digital fractional order differentiator. Signal Process. , 2359 - 2365
    16. 16)
      • Paluri, N.S.V., Sondur, S.: `Extrapolation based interval approach to compute the frequency responses of non-rational transfer functions with nonlinear parametric dependencies', Proc. IEEE Conf. Decision and Control, 2005, p. 6561–6566.
    17. 17)
      • B. Carlsson . Maximum flat digital differentiator. Electron. Lett. , 675 - 677
    18. 18)
      • T.W. Parks , J.H. McClellan . Chebyshev approximation for nonrecursive digital filters with linear phase. IEEE Trans. Circuit Theory , 189 - 194
    19. 19)
      • T.B. Deng , Y. Lian . Weighted-least-squares design of variable fractional-delay FIR filters using coefficient symmetry. IEEE Trans. Signal Process. , 3023 - 3038
    20. 20)
      • C.C. Tseng . Stable IIR digital differentiator design using iterative quadratic programming approach. Signal Process. , 857 - 866
    21. 21)
      • I.R. Khan , R. Ohba . New design of full band differentiators based on Taylor series. IEE Proc., Vis. Image Signal Process. , 185 - 189
    22. 22)
      • V.R. Chinni , C.R. Menyuk , P.K.A. Wai . Accurate solution of the paraxial wave equation using Richardson extrapolation. IEEE Photonics Technol. Lett. , 409 - 411
    23. 23)
      • K. Yamamura , K. Horiuchi . The use of extrapolation for the problem of computing accurate bifurcation values of periodic responses. IEEE Trans. Circuits Syst. , 628 - 631
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-spr_20070145
Loading

Related content

content/journals/10.1049/iet-spr_20070145
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading