PMID- 20686595
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20110209
LR  - 20181023
IS  - 1520-8532 (Electronic)
IS  - 1084-7529 (Linking)
VI  - 27
IP  - 8
DP  - 2010 Aug 1
TI  - Equivalence of linear canonical transform domains to fractional Fourier domains 
      and the bicanonical width product: a generalization of the space-bandwidth 
      product.
PG  - 1885-95
LID - 10.1364/JOSAA.27.001885 [doi]
AB  - 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.
FAU - Oktem, Figen S
AU  - Oktem FS
AD  - Department of Electrical Engineering, Bilkent University, TR-06800 Bilkent, 
      Ankara, Turkey. oktem1@illinois.edu
FAU - Ozaktas, Haldun M
AU  - Ozaktas HM
LA  - eng
PT  - Journal Article
PL  - United States
TA  - J Opt Soc Am A Opt Image Sci Vis
JT  - Journal of the Optical Society of America. A, Optics, image science, and vision
JID - 9800943
EDAT- 2010/08/06 06:00
MHDA- 2010/08/06 06:01
CRDT- 2010/08/06 06:00
PHST- 2010/08/06 06:00 [entrez]
PHST- 2010/08/06 06:00 [pubmed]
PHST- 2010/08/06 06:01 [medline]
AID - 204194 [pii]
AID - 10.1364/JOSAA.27.001885 [doi]
PST - ppublish
SO  - J Opt Soc Am A Opt Image Sci Vis. 2010 Aug 1;27(8):1885-95. doi: 
      10.1364/JOSAA.27.001885.