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

Signal reconstruction from multiple correlations: frequency- and time-domain approaches

Not Accessible

Your library or personal account may give you access

Abstract

One-dimensional (1-D) ultrashort laser signals cannot be recorded directly, although it is possible to detect their multiple correlations. The reconstruction of 1-D deterministic sampled signals from their multiple correlations is studied. A computationally efficient, fast-Fourier-transform-based, frequency-domain algorithm is described for simultaneously reconstructing the amplitude and the phase of a finite-duration signal. It is shown that, by modeling the Fourier transform of a discrete sequence as a pole-zero rational function, unique (modulo time shifts) signal recovery is possible from any multiple correlation of order greater than 2. The resulting time-domain algorithm uses all the nonredundant 1-D slices of a multiple-correlation sequence and applies to one- or two-sided, finite- or infinite-duration signals. The signal parameters are obtained in closed form by using a set of linear equations. Noise effects are studied theoretically and experimentally through simulated data. Both frequency-and time-domain algorithms are applicable to modeling and interpolation of raster-scanned images.

© 1989 Optical Society of America

Full Article  |  PDF Article
More Like This
Shift- and rotation-invariant object reconstruction using the bispectrum

Brian M. Sadler and Georgios B. Giannakis
J. Opt. Soc. Am. A 9(1) 57-69 (1992)

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 (5)

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 (83)

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