Frequency Limitations and Optimal Step-size
for the Two-point Central Difference Derivative Algorithm
with Applications to Human Eye Movement Data

Terry Bahill
Systems and Industrial Engineering
University of Arizona
Tucson, AZ 85721-0020
terry@sie.arizona.edu
© 1998-2004 Bahill

There are many algorithms for calculating derivatives. The two-point central difference algorithm is the simplest. Besides simplicity, the two most important characteristics of this algorithm are accuracy and frequency response. The frequency content of the data prescribes a lower limit on the sampling rate. The smoothness and accuracy of the data determine the optimal step-size. We discuss the low-pass filter characteristics of this algorithm and derive the optimal step-size for two types of human eye movement data. To calculate the velocity of fast (saccadic) eye movements, the algorithm should have a cutoff frequency of at least 74 hertz. For typical slow (smooth pursuit) eye movements a step-size of 25 or 50 msec is optimal.

References [25, and 26]. This lecture on signal processing is mathematical, and is suitable for engineers. It requires an overhead projector. This talk takes one hour.