Abstract

The bispectrum is the Fourier transform of the triple correlation, sometimes also referred to as triple product integral. We are concerned here with the bispectrum of the autotriple correlation. Bispectrum analysis can be used to solve phase problems in signal processing, since the knowledge of the bispectrum of a signal usually allows one to reconstruct both amplitude and phase of the Fourier transform signal. We present mathematical proof based on the theory of analytic functions and discuss the restrictions involved. A recursive algorithm is outlined for the reconstruction from sampled data. In addition, possibilities for noise reduction by averaging redundant information will be described. Examples are included for 1-D signals.

© 1984 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Bispectral analysis at low light levels and astronomical speckle masking

B. Wirnitzer
J. Opt. Soc. Am. A 2(1) 14-21 (1985)

Least-squares phase recovery from the bispectrum phase: an algorithm for a two-dimensional object

Hiroaki Takajo and Tohru Takahashi
J. Opt. Soc. Am. A 8(7) 1038-1047 (1991)

Bispectral magnitude and phase recovery using a wide bandwidth acousto-optic processor

Stacy K. Kniffen, Michael F. Becker, and Edward J. Powers
Appl. Opt. 31(8) 1015-1029 (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 OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA 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 OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA 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 OSA member, or as an authorized user of your institution.

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

Tables (2)

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

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

Equations (37)

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

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

Metrics

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

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