PubMed Health⌕ Search
Home/Archive/PubMed

PubMed · 7126687

Frequency limitations of the two-point central difference differentiation algorithm.

A T Bahill·J S Kallman·J E Lieberman
View original source ↗Export metadata ↓

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.

Explore related subjects

Eye MovementsHumansMathematicsModels, BiologicalSaccadesJournal ArticleResearch Support, U.S. Gov't, Non-P.H.S.Research Support, U.S. Gov't, P.H.S.

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

A T Bahill, J S Kallman, J E Lieberman. 1982. Frequency limitations of the two-point central difference differentiation algorithm.. https://doi.org/10.1007/bf00387207

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

PubMed1992

The perception of heading during eye movements.

When a person walks through a rigid environment while holding eyes and head fixed, the pattern of retinal motion flows radially away from a point, the focus of expansion (Fig. 1a). Under such conditions of translation, heading corresponds to the focus of expansion and people identify it readily. But when making an eye/head movement to track an object off to the side, retinal motion is no longer radial (Fig. 1b). Heading perception in such situations has been modelled in two ways. Extra-retinal models monitor the velocity of rotational movements through proprioceptive or efference information from the extraocular and neck muscles and use that information to discount rotation effects. Retinal-image models determine (and eliminate) rotational components from the retinal image alone. These models have been tested by measuring heading perception under two conditions. First, observers judged heading while tracking a point on a simulated ground plane. Second, they fixated a stationary point and the flow field simulated the effects of a tracking eye movement. Extra-retinal models predict poorer performance in the simulated condition because the eyes do not move. Retinal-image models predict no difference in performance because the two conditions produce identical patterns of retinal motion. Warren and Hannon observed similar performance and concluded that people do not require extra-retinal information to judge heading with eye/head movements present, but they used extremely slow tracking eye movements of 0.2-1.2 deg s-1; a moving observer frequently tracks objects at much higher rates (L. Stark, personal communication). Here we examine heading judgements at higher, more typical eye movement velocities and find that people require extra-retinal information about eye position to perceive heading accurately under many viewing conditions.

Eye Movements↗
PubMed1992

Residual vision in a scotoma: implications for blindsight.

Blindsight, the ability of some blind patients to describe attributes of stimuli they have no conscious awareness of seeing, has been attributed to a secondary (retinotectal) visual pathway. However, it has also been proposed that blindsight could be due to residual function within the primary (geniculostriate) visual pathway. Data have now been obtained that support the second alternative. With an image stabilizer ensuring the accurate retinal placement of stimuli, dense visual field mapping was carried out with a hemianopic patient. This perimetry revealed, embedded in the patient's scotoma, an isolated 1-degree island of residual vision that was not disclosed by conventional perimetric methods. Stimuli presented to this island could be detected and discriminated, although the subject reported he did not see them. The existence of this island of vision implies a corresponding island of functioning cortex within the patient's lesion. Other instances of blindsight may be mediated by similar islands of functioning cortex.

Eye Movements↗
PubMed1992

Hand-eye coordination during sequential tasks.

The small angle subtended by the human fovea places a premium on the ability to quickly and accurately direct the gaze to targets of interest. Thus the resultant saccadic eye fixations are a very instructive behaviour, revealing much about the underlying cognitive mechanisms that guide them. Of particular interest are the eye fixations used in hand-eye coordination. Such coordination has been extensively studied for single movements from a source location to a target location. In contrast, we have studied multiple fixations where the sources and targets are a function of a task and chosen dynamically by the subject according to task requirements. The task chosen is a copying task: subjects must copy a figure made up of contiguous coloured blocks as fast as possible. The main observation is that although eye fixations are used for the terminal phase of hand movements, they are used for other tasks before and after that phase. The analysis of the spatial and temporal details of these fixations suggests that the underlying decision process that moves the eyes leaves key decisions until just before they are required.

Eye Movements↗