Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Multidimensional-signal sample dependency at Nyquist densities

Not Accessible

Your library or personal account may give you access

Abstract

When a multidimensional signal is uniformly sampled, its spectrum is replicated. If the signal is band limited and the replications (1) contain regions that are identically zero and (2) are not aliased, then the samples are dependent. Indeed, lost samples can be regained from those remaining. In dimensions greater than one, there are spectral regions of support for which this is the case even when sampling is performed at the Nyquist (minimum) density (e.g., a circular spectral region of support in two dimensions). When the known samples are perturbed by additive noise, lost-sample restoration noise levels in certain cases can be obtained by simple geometrical observations in the frequency domain. The results are specifically applied to coherent and incoherent optical images of objects of finite extent obtained from imaging systems with circular pupils.

© 1986 Optical Society of America

Full Article  |  PDF Article
More Like This
Imaging sampling below the Nyquist density without aliasing

Kwan F. Cheung and Robert J. Marks
J. Opt. Soc. Am. A 7(1) 92-105 (1990)

Sampling below the Nyquist density using spectral subtiles

Robert J. Marks
J. Opt. Soc. Am. A 36(8) 1322-1332 (2019)

Sampling-theory analysis of spatial vision

Wilson S. Geisler and David B. Hamilton
J. Opt. Soc. Am. A 3(1) 62-70 (1986)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (7)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (46)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Metrics

Select as filters


Select Topics Cancel
© Copyright 2022 | Optica Publishing Group. All Rights Reserved