Advertisement

Biological Cybernetics

, Volume 45, Issue 1, pp 1–4 | Cite as

Frequency limitations of the two-point central difference differentiation algorithm

  • A. Terry Bahill
  • Jeffrey S. Kallman
  • Jon E. Lieberman
Article

Abstract

A two-point central difference algorithm is often used to calculate the derivative of a function. This estimate is only valid over a limited frequency range. Therefore, the algorithm can be modeled as an ideal differentiator in series with a low-pass filter. The filter cutoff frequency is a function of the time between the points. We discuss the accuracy and limitations of using this algorithm on human saccadic eye movement data. To calculate the velocity of saccadic eye movements the algorithm should have a cutoff frequency of 74 Hz or above.

Keywords

Cutoff Frequency Central Difference Movement Data Difference Differentiation Frequency Limitation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bahill, A.T.: Bioengineering: biomedical, medical, and clinical engineering. Englewood Cliffs, NJ: Prentice-Hall Inc. 1981Google Scholar
  2. Bahill, A.T., Brockenbrough, A.E., Troost, B.T.: Variability and development of a normative data base for saccadic eye movements. Invest. Ophthalmol. Vis. Sci. 21, 116–125 (1981)Google Scholar
  3. Hamming, R.W.: Digital filters. Englewood Cliffs, NJ: Prentice-Hall Inc. 1977, pp. 104–112Google Scholar
  4. Marble, A.E., McIntyre, C.M., Hastings-James, R., Hor, C.W.: A comparison of digital algorithms used in computing the derivative of left ventricular pressure. IEEE Trans. Biomed. Eng. 28, 524–529 (1981)Google Scholar
  5. Rabiner, L.R., Gold, B.: Theory and application of digital signal processing pp 164–170. Englewood Cliffs, NJ: Prentice-Hall Inc. 1975Google Scholar
  6. Tole, J.R., Oman, C.M., Michaels, D.L., Weiss, A.D., Young, L.R.: Nystagmus analysis using a microprocessor based instrument. In: Vestibular mechanisms in health and disease. VI. Extraordinary meeting of Barany Society, pp. 144–149, Hood, J.D. (ed). New York: Academic Press 1978Google Scholar
  7. Usui, S., Amidor, I.: Digital differentiation filters for biological signal processing. In: Proc. 8th Int. Cong. of Biomechanics. Nagoya, Japan 1981Google Scholar
  8. Young, D.M., Gregory, R.T.: A survey of numerical mathematics, Vol. 1, pp. 350–361. Reading, MA Addison-Wesley Publishing Co. 1972Google Scholar
  9. van der Tweel, L.H., Estevez, O., Strackee, J.: Measurement of evoked potentials. In: Evoked potentials, pp. 19–41, Barber, C. (ed). Baltimore: University Park Press 1980Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • A. Terry Bahill
    • 1
  • Jeffrey S. Kallman
    • 1
  • Jon E. Lieberman
    • 1
  1. 1.Biomedical Engineering Program, Department of Electrical EngineeringCarnegie-Mellon UniversityPittsburghUSA

Personalised recommendations