Improved discrete fractional Fourier transform

Soo-Chang Pei; Min-Hung Yeh

doi:10.1364/OL.22.001047

Improved discrete fractional Fourier transform

Soo-Chang Pei and Min-Hung Yeh

Optics Letters
Vol. 22,
Issue 14,
pp. 1047-1049
(1997)
•https://doi.org/10.1364/OL.22.001047

Get Citation
Copy Citation Text
Soo-Chang Pei and Min-Hung Yeh, "Improved discrete fractional Fourier transform," Opt. Lett. 22, 1047-1049 (1997)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Get PDF (336 KB)
Set citation alerts
Save article

Related Topics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: March 11, 1997
- Published: July 15, 1997

Not Accessible

Your account may give you access

Abstract

The fractional Fourier transform is a useful mathematical operation that generalizes the well-known continuous Fourier transform. Several discrete fractional Fourier transforms (DFRFT’s) have been developed, but their results do not match those of the continuous case. We propose a new DFRFT. This improved DFRFT provides transforms similar to those of the continuous fractional Fourier transform and also retains the rotation properties.

Full Article | PDF Article

OSA Recommended Articles

Discrete fractional Fourier transform as a fast algorithm for evaluating the diffraction pattern of pulsed radiation

Magdy Tawfik Hanna, Amr Mohamed Shaarawi, Nabila Philip Attalla Seif, and Waleed Abd El Maguid Ahmed
J. Opt. Soc. Am. A 28(8) 1610-1619 (2011)

Fractional Hankel transform studied by charge-amplitude state representations and complex fractional Fourier transformation

Hong-yi Fan
Opt. Lett. 28(22) 2177-2179 (2003)

Fractional discrete Fourier transforms

Zheng-Tao Deng, H. John Caulfield, and Marius Schamschula
Opt. Lett. 21(18) 1430-1432 (1996)

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 (3)

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 (11)

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

$N$	1	$- j$	$- 1$	$j$
$4 m$	$m + 1$	$m$	$m$	$m - 1$
$4 m + 1$	$m + 1$	$m$	$m$	$m$
$4 m + 2$	$m + 1$	$m$	$m + 1$	$m$
$4 m + 3$	$m + 1$	$m + 1$	$m + 1$	$m$

$N$	DFRFT Eigenvalues
$4 m$	$exp (- jk α), k = 0, 1, 2, \dots, 4 m - 2, 4 m$
$4 m + 1$	$exp (- jk α), k = 0, 1, 2, \dots, 4 m - 1, 4 m$
$4 m + 2$	$exp (- jk α), k = 0, 1, 2, \dots, 4 m, 4 m + 2$
$4 m + 3$	$exp (- jk α), k = 0, 1, 2, \dots, 4 m + 1, 4 m + 2$

$N$	1	$- j$	$- 1$	$j$
$4 m$	$m + 1$	$m$	$m$	$m - 1$
$4 m + 1$	$m + 1$	$m$	$m$	$m$
$4 m + 2$	$m + 1$	$m$	$m + 1$	$m$
$4 m + 3$	$m + 1$	$m + 1$	$m + 1$	$m$

$N$	DFRFT Eigenvalues
$4 m$	$exp (- jk α), k = 0, 1, 2, \dots, 4 m - 2, 4 m$
$4 m + 1$	$exp (- jk α), k = 0, 1, 2, \dots, 4 m - 1, 4 m$
$4 m + 2$	$exp (- jk α), k = 0, 1, 2, \dots, 4 m, 4 m + 2$
$4 m + 3$	$exp (- jk α), k = 0, 1, 2, \dots, 4 m + 1, 4 m + 2$

Abstract

References

Cited By

Figures (3)

Tables (2)

Equations (11)

Metrics

Login or Create Account