Article detail · 2010
Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space–bandwidth product
Journal
Journal of the Optical Society of America AISSN 1084-7529
The ISSN points to another catalog journal; the name is from the YÖKSİS record.
- Year
- 2010
- Type
- article
Data source split
- YÖKSİS YÖKSİS article record
- YÖKSİS venue Journal of the Optical Society of America A
- Catalog match (ISSN) Journal of the Optical Society of America A: Optics and Image Science, and Vision
- OpenAlex OpenAlex enrichment (abstract, citations, topics)
Abstract
OpenAlex · English
Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.
Topics
Citations
OpenAlex cited_by_count. Not a WoS or Scopus citation count; those sources have no separate column here.
42 citations
OpenAlex cited_by_count (cache / database)
8 publications in the local catalog that cite this work (OpenAlex reference match; not the full global list).
- Phase-space window and degrees of freedom of optical systems with multiple apertures 2013
- Fast Algorithms for Digital Computation of Linear Canonical Transforms 2015
- Linear Canonical Domains and Degrees of Freedom of Signals and Systems 2015
- Degrees of freedom of optical systems and signals with applications to sampling and system simulation 2013
- Relationship between the beam propagation method and linear canonical and fractional Fourier transforms 2022
- Fast and accurate linear canonical transform algorithms 2015
- Effect of spatial distribution of partial information on the accurate recovery of optical wave fields 2017
- Linear canonical transforms, degrees of freedom, and sampling in optical signals and systems 2014