TY - JOUR
T1 - Two-dimensional OLCT of angularly periodic functions in polar coordinates
AU - Zhao, Hui
AU - Li, Bing Zhao
N1 - Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2023/4/15
Y1 - 2023/4/15
N2 - Searching for novel signal processing theories and methods has always been a research hotspot in the field of modern signal processing. The existing transform methods for dealing with non-stationary signals are based on traditional Cartesian coordinates, which are very inconvenient to deal with signals naturally described by polar coordinates. This paper studies two-dimensional offset linear canonical transform (OLCT) in polar coordinates. Firstly, the definition of the two-dimensional OLCT in polar coordinates is proposed, and the offset linear canonical Hankel transform (OLCHT) formula is derived. Secondly, the relationship between the OLCT and the OLCHT is revealed through the angular periodic function. Then, some properties of the two-dimensional OLCT in polar coordinates are proved based on the mentioned relationship. Finally, the proposed two-dimensional OLCT is applied in the computed tomography. The effectiveness and feasibility of the proposed method are verified by simulation experiments.
AB - Searching for novel signal processing theories and methods has always been a research hotspot in the field of modern signal processing. The existing transform methods for dealing with non-stationary signals are based on traditional Cartesian coordinates, which are very inconvenient to deal with signals naturally described by polar coordinates. This paper studies two-dimensional offset linear canonical transform (OLCT) in polar coordinates. Firstly, the definition of the two-dimensional OLCT in polar coordinates is proposed, and the offset linear canonical Hankel transform (OLCHT) formula is derived. Secondly, the relationship between the OLCT and the OLCHT is revealed through the angular periodic function. Then, some properties of the two-dimensional OLCT in polar coordinates are proved based on the mentioned relationship. Finally, the proposed two-dimensional OLCT is applied in the computed tomography. The effectiveness and feasibility of the proposed method are verified by simulation experiments.
KW - Convolution theorem
KW - Offset linear canonical Hankel transform
KW - Offset linear canonical transform
KW - Polar coordinates
KW - Spatial shift theorem
UR - http://www.scopus.com/inward/record.url?scp=85146052886&partnerID=8YFLogxK
U2 - 10.1016/j.dsp.2022.103905
DO - 10.1016/j.dsp.2022.103905
M3 - Article
AN - SCOPUS:85146052886
SN - 1051-2004
VL - 134
JO - Digital Signal Processing: A Review Journal
JF - Digital Signal Processing: A Review Journal
M1 - 103905
ER -