PMID- 32543595
OWN - NLM
STAT- PubMed-not-MEDLINE
LR  - 20200617
IS  - 1520-8532 (Electronic)
IS  - 1084-7529 (Linking)
VI  - 37
IP  - 6
DP  - 2020 Jun 1
TI  - Discrete normalized Bargmann transform through the gyrator transform.
PG  - 951-958
LID - 10.1364/JOSAA.387945 [doi]
AB  - Linear canonical transforms (LCTs) are important in several areas of signal 
      processing; in particular, they were extended to complex-valued parameters to 
      describe optical systems. A special case of these complex LCTs is the Bargmann 
      transform. Recently, Pei and Huang [J. Opt. Soc. Am. A34, 18 
      (2017)JOAOD60740-323210.1364/JOSAA.34.000018] presented a normalization of the 
      Bargmann transform so that it becomes possible to delimit it near infinity. In 
      this paper, we follow the Pei-Huang algorithm to introduce the discrete 
      normalized Bargmann transform by the relationship between Bargmann and gyrator 
      transforms in the SU(2) finite harmonic oscillator model, and we compare it with 
      the discrete Bargmann transform based on coherent states of the SU(2) oscillator 
      model. This transformation is invertible and unitary. We show that, as in the 
      continuous analog, the discrete normalized Bargmann transform converts the 
      Hermite-Kravchuk functions into Laguerre-Kravchuk functions. In addition, we 
      demonstrate that the discrete su(1,1) repulsive oscillator functions 
      self-reproduce under this discrete transform with little error. Finally, in the 
      space spanned by the wave functions of the SU(2) harmonic oscillator, we find 
      that the discrete normalized Bargmann transform commutes with the fractional 
      Fourier-Kravchuk transform.
FAU - Uriostegui, Kenan
AU  - Uriostegui K
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
SB  - IM
EDAT- 2020/06/17 06:00
MHDA- 2020/06/17 06:01
CRDT- 2020/06/17 06:00
PHST- 2020/06/17 06:00 [entrez]
PHST- 2020/06/17 06:00 [pubmed]
PHST- 2020/06/17 06:01 [medline]
AID - 431759 [pii]
AID - 10.1364/JOSAA.387945 [doi]
PST - ppublish
SO  - J Opt Soc Am A Opt Image Sci Vis. 2020 Jun 1;37(6):951-958. doi: 
      10.1364/JOSAA.387945.