Sampling Theorems Associated with Offset Linear Canonical Transform by Polar Coordinates

Hui Zhao; Bing Zhao Li

doi:10.3390/fractalfract8100559

Sampling Theorems Associated with Offset Linear Canonical Transform by Polar Coordinates

Hui Zhao, Bing Zhao Li^*

^*Corresponding author for this work

School of Mathematics and Statistics

Shijiazhuang Tiedao University

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The sampling theorem for the offset linear canonical transform (OLCT) of bandlimited functions in polar coordinates is an important signal analysis tool in many fields of signal processing and optics. This paper investigates two sampling theorems for interpolating bandlimited and highest frequency bandlimited functions in the OLCT and offset linear canonical Hankel transform (OLCHT) domains by polar coordinates. Based on the classical Stark’s interpolation formulas, we derive the sampling theorems for bandlimited functions in the OLCT and OLCHT domains, respectively. The first interpolation formula is concise and applicable. Due to the consistency of the OLCHT order, the second interpolation formula is superior to the first interpolation formula in computational complexity.

Original language	English
Article number	559
Journal	Fractal and Fractional
Volume	8
Issue number	10
DOIs	https://doi.org/10.3390/fractalfract8100559
Publication status	Published - Oct 2024

Keywords

offset linear canonical Hankel transform
offset linear canonical transform
polar coordinates
sampling theorems

Access to Document

10.3390/fractalfract8100559

Cite this

@article{318282edfc4e4b31be585071cd4dd65f,

title = "Sampling Theorems Associated with Offset Linear Canonical Transform by Polar Coordinates",

abstract = "The sampling theorem for the offset linear canonical transform (OLCT) of bandlimited functions in polar coordinates is an important signal analysis tool in many fields of signal processing and optics. This paper investigates two sampling theorems for interpolating bandlimited and highest frequency bandlimited functions in the OLCT and offset linear canonical Hankel transform (OLCHT) domains by polar coordinates. Based on the classical Stark{\textquoteright}s interpolation formulas, we derive the sampling theorems for bandlimited functions in the OLCT and OLCHT domains, respectively. The first interpolation formula is concise and applicable. Due to the consistency of the OLCHT order, the second interpolation formula is superior to the first interpolation formula in computational complexity.",

keywords = "offset linear canonical Hankel transform, offset linear canonical transform, polar coordinates, sampling theorems",

author = "Hui Zhao and Li, {Bing Zhao}",

note = "Publisher Copyright: {\textcopyright} 2024 by the authors.",

year = "2024",

month = oct,

doi = "10.3390/fractalfract8100559",

language = "English",

volume = "8",

journal = "Fractal and Fractional",

issn = "2504-3110",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "10",

}

TY - JOUR

T1 - Sampling Theorems Associated with Offset Linear Canonical Transform by Polar Coordinates

AU - Zhao, Hui

AU - Li, Bing Zhao

PY - 2024/10

Y1 - 2024/10

N2 - The sampling theorem for the offset linear canonical transform (OLCT) of bandlimited functions in polar coordinates is an important signal analysis tool in many fields of signal processing and optics. This paper investigates two sampling theorems for interpolating bandlimited and highest frequency bandlimited functions in the OLCT and offset linear canonical Hankel transform (OLCHT) domains by polar coordinates. Based on the classical Stark’s interpolation formulas, we derive the sampling theorems for bandlimited functions in the OLCT and OLCHT domains, respectively. The first interpolation formula is concise and applicable. Due to the consistency of the OLCHT order, the second interpolation formula is superior to the first interpolation formula in computational complexity.

AB - The sampling theorem for the offset linear canonical transform (OLCT) of bandlimited functions in polar coordinates is an important signal analysis tool in many fields of signal processing and optics. This paper investigates two sampling theorems for interpolating bandlimited and highest frequency bandlimited functions in the OLCT and offset linear canonical Hankel transform (OLCHT) domains by polar coordinates. Based on the classical Stark’s interpolation formulas, we derive the sampling theorems for bandlimited functions in the OLCT and OLCHT domains, respectively. The first interpolation formula is concise and applicable. Due to the consistency of the OLCHT order, the second interpolation formula is superior to the first interpolation formula in computational complexity.

KW - offset linear canonical Hankel transform

KW - offset linear canonical transform

KW - polar coordinates

KW - sampling theorems

UR - http://www.scopus.com/inward/record.url?scp=85207667360&partnerID=8YFLogxK

U2 - 10.3390/fractalfract8100559

DO - 10.3390/fractalfract8100559

M3 - Article

AN - SCOPUS:85207667360

SN - 2504-3110

VL - 8

JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 10

M1 - 559

ER -

Sampling Theorems Associated with Offset Linear Canonical Transform by Polar Coordinates

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this