Octonion quadratic-phase Fourier transform: inequalities, uncertainty principles, and examples

In this article, we define the octonion quadratic-phase Fourier transform (OQPFT) and derive its inversion formula, including its fundamental properties such as linearity, parity, modulation, and shifting. We also establish its relationship with the quaternion quadratic-phase Fourier transform (QQPF...

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Veröffentlicht in:Journal of inequalities and applications Jg. 2024; H. 1; S. 134 - 52
Hauptverfasser: Kumar, Manish, Bhawna
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 16.10.2024
Springer Nature B.V
SpringerOpen
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Data compression
Fourier transform
Fourier transforms
Inequalities
Inequality
Integral transforms
Investigations
Lie groups
Mathematics
Mathematics and Statistics
Octonion quadratic-phase Fourier transform
Principles
Quaternions
Sharp inequalities
Signal processing
Uncertainty principles
Wavelet transforms
26A42
Sharp inequalities
Uncertainty principles
42B10
Octonion quadratic-phase Fourier transform
Fourier transform
26D15
ISSN:1029-242X, 1025-5834, 1029-242X
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Abstract In this article, we define the octonion quadratic-phase Fourier transform (OQPFT) and derive its inversion formula, including its fundamental properties such as linearity, parity, modulation, and shifting. We also establish its relationship with the quaternion quadratic-phase Fourier transform (QQPFT). Further, we derive the Parseval formula and the Riemann–Lebesgue lemma using this transform. Furthermore, we formulate two important inequalities (sharp Pitt’s and sharp Hausdorff–Young’s inequalities) and three main uncertainty principles (logarithmic, Donoho–Stark’s, and Heisenberg’s uncertainty principles) for the OQPFT. To complete our investigation, we construct three elementary examples of signal theory with graphical interpretations to illustrate the use of OQPFT and discuss their particular cases.
AbstractList In this article, we define the octonion quadratic-phase Fourier transform (OQPFT) and derive its inversion formula, including its fundamental properties such as linearity, parity, modulation, and shifting. We also establish its relationship with the quaternion quadratic-phase Fourier transform (QQPFT). Further, we derive the Parseval formula and the Riemann–Lebesgue lemma using this transform. Furthermore, we formulate two important inequalities (sharp Pitt’s and sharp Hausdorff–Young’s inequalities) and three main uncertainty principles (logarithmic, Donoho–Stark’s, and Heisenberg’s uncertainty principles) for the OQPFT. To complete our investigation, we construct three elementary examples of signal theory with graphical interpretations to illustrate the use of OQPFT and discuss their particular cases.
Abstract In this article, we define the octonion quadratic-phase Fourier transform (OQPFT) and derive its inversion formula, including its fundamental properties such as linearity, parity, modulation, and shifting. We also establish its relationship with the quaternion quadratic-phase Fourier transform (QQPFT). Further, we derive the Parseval formula and the Riemann–Lebesgue lemma using this transform. Furthermore, we formulate two important inequalities (sharp Pitt’s and sharp Hausdorff–Young’s inequalities) and three main uncertainty principles (logarithmic, Donoho–Stark’s, and Heisenberg’s uncertainty principles) for the OQPFT. To complete our investigation, we construct three elementary examples of signal theory with graphical interpretations to illustrate the use of OQPFT and discuss their particular cases.
ArticleNumber 134
Author Bhawna
Kumar, Manish
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  surname: Bhawna
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  organization: Department of Mathematics, Birla Institute of Technology and Science-Pilani
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Cites_doi 10.3390/math11194101
10.1002/mma.8667
10.1007/s11868-024-00590-6
10.1016/j.image.2021.116574
10.1049/iet-ipr.2018.5440
10.1016/j.sigpro.2008.04.012
10.1002/mma.5353
10.3390/math11133002
10.1016/j.jmaa.2014.10.003
10.1016/j.prime.2023.100162
10.1080/10652469.2015.1114482
10.1007/s40819-020-00917-z
10.3390/math11030677
10.3390/math11122742
10.1186/1687-6180-2012-120
10.1002/9781118930908
10.1016/j.sigpro.2021.108233
10.1201/9781439864180
10.1007/BF02649110
10.1007/s00009-023-02403-4
10.1142/8456
10.3390/math11051158
10.1002/mma.6018
10.1002/mma.7692
10.1002/mma.7417
10.1007/s00006-018-0828-0
10.1016/j.jmaa.2015.09.068
10.1515/gmj-2022-2158
10.1016/j.ijleo.2016.09.069
10.1109/LSP.2009.2026107
10.1007/BF02384339
10.1364/JOSAA.25.000647
10.1007/s00006-022-01244-w
10.1186/s13660-022-02873-2
10.1016/j.optcom.2011.10.019
10.1016/j.sigpro.2008.09.002
10.1007/s40314-020-01373-7
10.1201/9781420003451
10.3390/math11051235
10.1002/mma.4271
10.1137/1033097
10.1137/0149053
10.1016/j.jmaa.2019.123730
10.3390/math11020344
10.1007/s00034-018-0863-z
10.1017/CBO9780511524479
10.1007/s43034-023-00280-2
10.1007/s00006-019-1020-x
10.2298/FIL2313155P
10.1016/j.sigpro.2016.11.021
10.1016/j.sigpro.2019.06.015
10.1007/s11868-012-0047-8
10.1080/10652469.2019.1707816
10.1007/s11760-016-0965-7
10.1063/1.1665805
10.1002/mma.9440
10.1002/mma.9126
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Keywords 26A42
Sharp inequalities
Uncertainty principles
42B10
Octonion quadratic-phase Fourier transform
Fourier transform
26D15
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References Pathak, Prasad, Kumar (CR54) 2012; 3
Chen, Yu, Tian, Li, Wang, Sun (CR15) 2018; 12
Bas, Le Bihan, Chassery (CR8) 2003
Moshinsky, Quesne (CR48) 1971; 12
Chen, Kou, Liu (CR16) 2015; 423
Huo (CR34) 2019; 38
Prasad, Kumar, Choudhury (CR56) 2012; 285
Zhang, Li (CR72) 2018; 28
CR70
Mani, Gnanaprakasam, Guran, George, Mitrović (CR46) 2023; 11
Bhat, Dar, Zayed, Bhat (CR11) 2023; 11
Achak, Abouelaz, Daher, Safouane (CR1) 2019; 29
Gao, Li (CR23) 2021; 188
Shi, Han, Zhang (CR64) 2016; 10
Bansal, Kumar, Bansal (CR7) 2023; 14
Healy, Kutay, Ozaktas, Sheridan (CR31) 2015
Wei, Ran, Li, Ma, Tan (CR68) 2009; 16
CR2
Ell, Le Bihan, Sangwine (CR20) 2014
Okubo (CR50) 1995
Yang, Kou Kit (CR69) 2016; 27
Bailey, Swarztrauber (CR6) 1991; 33
Donoho, Stark (CR18) 1989; 49
Zhou, Yang (CR73) 2024; 44
Li, Bi, Li (CR41) 2012; 2012
Kou, Morais (CR36) 2014; 247
Mani, Haque, Gnanaprakasam, Ege, Mlaiki (CR47) 2023; 11
Guanlei, Xiaotong, Xiaogang (CR25) 2008; 88
Kumar (CR39) 2020; 6
Sharma, Prasad (CR62) 2022; 29
Gnanaprakasam, Mani, Ege, Aloqaily, Mlaiki (CR24) 2023; 11
Ozaktas, Kutay, Mendlovic (CR52) 1999
Lian (CR43) 2019; 164
Błaszczyk, Snopek (CR13) 2017; 136
Zhu, Zheng (CR74) 2021; 44
Huo, Sun, Xiao (CR35) 2019; 42
Błaszczyk (CR12) 2020; 39
Beckner (CR9) 1995; 123
Osgood (CR51) 2019
Nallaselli, Gnanaprakasam, Mani, Mitrović, Aloqaily, Mlaiki (CR49) 2023; 11
Ozaktas, Zalevsky, Kutay (CR53) 2001
Bhat, Dar (CR10) 2023; 4
Dray, Manogue (CR19) 2015
Zayed, Haoui Youssef (CR71) 2023; 46
Roopkumar (CR58) 2016; 127
Kou, Yang, Zou (CR38) 2017; 40
Boggiatto, Carypis, Oliaro (CR14) 2016; 434
Bahri, Shah, Tantary (CR5) 2020; 31
Mani, Gnanaprakasam, Ege, Aloqaily, Mlaiki (CR45) 2023; 11
Sneddon (CR65) 1995
Folland, Sitaram (CR21) 1997; 3
Conway, Smith (CR17) 2003
Bahri, Ashino (CR4) 2016
Sabinin, Sbitneva, Shestakov (CR59) 2006
Hörmander (CR33) 1991; 29
Shah, Nisar, Lone, Tantary (CR61) 2021; 44
Pradhana, Kumar (CR55) 2023; 37
Havin, Jöricke (CR30) 2012
CR29
Prasad, Sharma (CR57) 2020; 43
CR28
Titchmarsh (CR67) 1948
Hogan, Lakey (CR32) 2005
Kou, Ou, Morais (CR37) 2013
Shah, Lone, Nisar, Abdeljawad (CR60) 2022; 2022
CR63
Stern (CR66) 2008; 25
Gao (CR22) 2024; 15
Lian (CR44) 2020; 484
Hamadi, Ghandouri, Hafirassou (CR27) 2023; 20
Li, Fei (CR40) 2023; 33
Bahri, Abdul Karim (CR3) 2023; 11
Guanlei, Xiaotong, Xiaogang (CR26) 2009; 89
Li, Li, Qi (CR42) 2022; 101
D. Wei (3213_CR68) 2009; 16
G. Mani (3213_CR45) 2023; 11
A. Prasad (3213_CR56) 2012; 285
M.Y. Bhat (3213_CR10) 2023; 4
M. Moshinsky (3213_CR48) 1971; 12
Y. Zhou (3213_CR73) 2024; 44
M. Bahri (3213_CR4) 2016
H. Huo (3213_CR34) 2019; 38
P. Boggiatto (3213_CR14) 2016; 434
X. Zhu (3213_CR74) 2021; 44
A. Achak (3213_CR1) 2019; 29
Y. Yang (3213_CR69) 2016; 27
X. Guanlei (3213_CR25) 2008; 88
Ł. Błaszczyk (3213_CR13) 2017; 136
P.B. Sharma (3213_CR62) 2022; 29
M. Bahri (3213_CR5) 2020; 31
K.I. Kou (3213_CR37) 2013
L. Sabinin (3213_CR59) 2006
M.Y. Bhat (3213_CR11) 2023; 11
W.-B. Gao (3213_CR22) 2024; 15
H.M. Ozaktas (3213_CR52) 1999
J. Shi (3213_CR64) 2016; 10
X. Guanlei (3213_CR26) 2009; 89
A. Stern (3213_CR66) 2008; 25
3213_CR63
P. Bas (3213_CR8) 2003
L. Hörmander (3213_CR33) 1991; 29
T. Pradhana (3213_CR55) 2023; 37
B. Chen (3213_CR15) 2018; 12
X. Li (3213_CR41) 2012; 2012
R. Pathak (3213_CR54) 2012; 3
K.I. Kou (3213_CR38) 2017; 40
P. Bansal (3213_CR7) 2023; 14
J.H. Conway (3213_CR17) 2003
P. Lian (3213_CR44) 2020; 484
G. Mani (3213_CR47) 2023; 11
D.L. Donoho (3213_CR18) 1989; 49
H. Huo (3213_CR35) 2019; 42
H.M. Ozaktas (3213_CR53) 2001
3213_CR29
3213_CR28
M. Kumar (3213_CR39) 2020; 6
G. Nallaselli (3213_CR49) 2023; 11
A.J. Gnanaprakasam (3213_CR24) 2023; 11
Z.-W. Li (3213_CR42) 2022; 101
F.A. Shah (3213_CR61) 2021; 44
3213_CR70
G.B. Folland (3213_CR21) 1997; 3
Ł. Błaszczyk (3213_CR12) 2020; 39
W. Beckner (3213_CR9) 1995; 123
N.B. Hamadi (3213_CR27) 2023; 20
F.A. Shah (3213_CR60) 2022; 2022
3213_CR2
Y.-N. Zhang (3213_CR72) 2018; 28
V. Havin (3213_CR30) 2012
J.J. Healy (3213_CR31) 2015
T. Dray (3213_CR19) 2015
R. Roopkumar (3213_CR58) 2016; 127
S. Li (3213_CR40) 2023; 33
E.C. Titchmarsh (3213_CR67) 1948
D.H. Bailey (3213_CR6) 1991; 33
W.-B. Gao (3213_CR23) 2021; 188
T.A. Ell (3213_CR20) 2014
G. Mani (3213_CR46) 2023; 11
B.G. Osgood (3213_CR51) 2019
L.-P. Chen (3213_CR16) 2015; 423
I.N. Sneddon (3213_CR65) 1995
K.I. Kou (3213_CR36) 2014; 247
J.A. Hogan (3213_CR32) 2005
S. Okubo (3213_CR50) 1995
A. Prasad (3213_CR57) 2020; 43
P. Lian (3213_CR43) 2019; 164
M. Bahri (3213_CR3) 2023; 11
M. Zayed (3213_CR71) 2023; 46
References_xml – volume: 11
  issue: 19
  year: 2023
  ident: CR46
  article-title: Some results in fuzzy b-metric space with b-triangular property and applications to Fredholm integral equations and dynamic programming
  publication-title: Mathematics
  doi: 10.3390/math11194101
– ident: CR70
– volume: 46
  start-page: 2651
  issue: 2
  year: 2023
  end-page: 2666
  ident: CR71
  article-title: The uncertainty principle for the octonion Fourier transform
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.8667
– volume: 15
  start-page: 1
  issue: 2
  year: 2024
  end-page: 19
  ident: CR22
  article-title: Uncertainty principles for the biquaternion offset linear canonical transform
  publication-title: J. Pseudo-Differ. Oper. Appl.
  doi: 10.1007/s11868-024-00590-6
– volume: 101
  year: 2022
  ident: CR42
  article-title: Two-dimensional quaternion linear canonical series for color images
  publication-title: Signal Process. Image Commun.
  doi: 10.1016/j.image.2021.116574
– volume: 12
  start-page: 2238
  issue: 12
  year: 2018
  end-page: 2249
  ident: CR15
  article-title: Multiple-parameter fractional quaternion Fourier transform and its application in colour image encryption
  publication-title: IET Image Process.
  doi: 10.1049/iet-ipr.2018.5440
– volume: 88
  start-page: 2511
  issue: 10
  year: 2008
  end-page: 2517
  ident: CR25
  article-title: Fractional quaternion Fourier transform, convolution and correlation
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2008.04.012
– volume: 42
  start-page: 466
  issue: 2
  year: 2019
  end-page: 474
  ident: CR35
  article-title: Uncertainty principles associated with the offset linear canonical transform
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.5353
– volume: 11
  issue: 13
  year: 2023
  ident: CR11
  article-title: Convolution, correlation and uncertainty principle in the one-dimensional quaternion quadratic-phase Fourier transform domain
  publication-title: Mathematics
  doi: 10.3390/math11133002
– volume: 423
  start-page: 681
  issue: 1
  year: 2015
  end-page: 700
  ident: CR16
  article-title: Pitt’s inequality and the uncertainty principle associated with the quaternion Fourier transform
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2014.10.003
– volume: 4
  year: 2023
  ident: CR10
  article-title: Quadratic phase S-transform: properties and uncertainty principles
  publication-title: e-Prime-Adv. Electr. Eng. Electron. Energy
  doi: 10.1016/j.prime.2023.100162
– volume: 123
  start-page: 1897
  issue: 6
  year: 1995
  end-page: 1905
  ident: CR9
  article-title: Pitt’s inequality and the uncertainty principle
  publication-title: Proc. Am. Math. Soc.
– volume: 247
  start-page: 675
  year: 2014
  end-page: 688
  ident: CR36
  article-title: Asymptotic behaviour of the quaternion linear canonical transform and the Bochner–Minlos theorem
  publication-title: Appl. Math. Comput.
– volume: 27
  start-page: 213
  issue: 3
  year: 2016
  end-page: 226
  ident: CR69
  article-title: Novel uncertainty principles associated with 2d quaternion Fourier transforms
  publication-title: Integral Transforms Spec. Funct.
  doi: 10.1080/10652469.2015.1114482
– ident: CR29
– volume: 6
  issue: 6
  year: 2020
  ident: CR39
  article-title: A new class of pseudo-differential operators involving linear canonical transform
  publication-title: Int. J. Appl. Comput. Math.
  doi: 10.1007/s40819-020-00917-z
– year: 1995
  ident: CR65
  publication-title: Fourier Transforms
– volume: 11
  issue: 3
  year: 2023
  ident: CR24
  article-title: New fixed point results in orthogonal b-metric spaces with related applications
  publication-title: Mathematics
  doi: 10.3390/math11030677
– year: 2016
  ident: CR4
  article-title: A simplified proof of uncertainty principle for quaternion linear canonical transform
  publication-title: Abstract and Applied Analysis
– volume: 11
  issue: 12
  year: 2023
  ident: CR47
  article-title: The study of bicomplex-valued controlled metric spaces with applications to fractional differential equations
  publication-title: Mathematics
  doi: 10.3390/math11122742
– volume: 2012
  start-page: 1
  year: 2012
  end-page: 13
  ident: CR41
  article-title: On uncertainty principle of the local polynomial Fourier transform
  publication-title: EURASIP J. Adv. Signal Process.
  doi: 10.1186/1687-6180-2012-120
– year: 2014
  ident: CR20
  publication-title: Quaternion Fourier Transforms for Signal and Image Processing
  doi: 10.1002/9781118930908
– volume: 188
  year: 2021
  ident: CR23
  article-title: The octonion linear canonical transform: definition and properties
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2021.108233
– year: 2019
  ident: CR51
  publication-title: Lectures on the Fourier Transform and Its Applications
– year: 2003
  ident: CR17
  publication-title: On Quaternions and Octonions
  doi: 10.1201/9781439864180
– volume: 3
  start-page: 207
  year: 1997
  end-page: 238
  ident: CR21
  article-title: The uncertainty principle: a mathematical survey
  publication-title: J. Fourier Anal. Appl.
  doi: 10.1007/BF02649110
– volume: 20
  issue: 4
  year: 2023
  ident: CR27
  article-title: Beckner logarithmic uncertainty principle for the Stockwell transform associated with the singular partial differential operators
  publication-title: Mediterr. J. Math.
  doi: 10.1007/s00009-023-02403-4
– year: 2015
  ident: CR19
  publication-title: The Geometry of the Octonions
  doi: 10.1142/8456
– volume: 11
  issue: 5
  year: 2023
  ident: CR45
  article-title: Fixed point results in -algebra-valued partial b-metric spaces with related application
  publication-title: Mathematics
  doi: 10.3390/math11051158
– year: 2013
  ident: CR37
  article-title: On uncertainty principle for quaternionic linear canonical transform
  publication-title: Abstract and Applied Analysis
– year: 2001
  ident: CR53
  publication-title: The Fractional Fourier Transform with Applications in Optics and Signal Processing
– volume: 43
  start-page: 1953
  issue: 4
  year: 2020
  end-page: 1969
  ident: CR57
  article-title: The quadratic-phase Fourier wavelet transform
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.6018
– volume: 44
  start-page: 14236
  issue: 18
  year: 2021
  end-page: 14255
  ident: CR74
  article-title: Uncertainty principles for the two-sided offset quaternion linear canonical transform
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.7692
– volume: 44
  start-page: 10416
  issue: 13
  year: 2021
  end-page: 10431
  ident: CR61
  article-title: Uncertainty principles for the quadratic-phase Fourier transforms
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.7417
– volume: 28
  start-page: 1
  year: 2018
  end-page: 14
  ident: CR72
  article-title: Novel uncertainty principles for two-sided quaternion linear canonical transform
  publication-title: Adv. Appl. Clifford Algebras
  doi: 10.1007/s00006-018-0828-0
– volume: 434
  start-page: 1489
  issue: 2
  year: 2016
  end-page: 1503
  ident: CR14
  article-title: Two aspects of the Donoho-Stark uncertainty principle
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2015.09.068
– volume: 29
  start-page: 595
  issue: 4
  year: 2022
  end-page: 602
  ident: CR62
  article-title: Convolution and product theorems for the quadratic-phase Fourier transform
  publication-title: Georgian Math. J.
  doi: 10.1515/gmj-2022-2158
– volume: 127
  start-page: 11657
  issue: 24
  year: 2016
  end-page: 11661
  ident: CR58
  article-title: Quaternionic one-dimensional fractional Fourier transform
  publication-title: Optik
  doi: 10.1016/j.ijleo.2016.09.069
– volume: 16
  start-page: 853
  issue: 10
  year: 2009
  end-page: 856
  ident: CR68
  article-title: A convolution and product theorem for the linear canonical transform
  publication-title: IEEE Signal Process. Lett.
  doi: 10.1109/LSP.2009.2026107
– year: 2012
  ident: CR30
  publication-title: The Uncertainty Principle in Harmonic Analysis
– ident: CR2
– volume: 29
  start-page: 237
  issue: 1–2
  year: 1991
  end-page: 240
  ident: CR33
  article-title: A uniqueness theorem of Beurling for Fourier transform pairs
  publication-title: Ark. Mat.
  doi: 10.1007/BF02384339
– volume: 25
  start-page: 647
  issue: 3
  year: 2008
  end-page: 652
  ident: CR66
  article-title: Uncertainty principles in linear canonical transform domains and some of their implications in optics
  publication-title: J. Opt. Soc. Am. A
  doi: 10.1364/JOSAA.25.000647
– volume: 33
  issue: 1
  year: 2023
  ident: CR40
  article-title: Pitt’s inequality and logarithmic uncertainty principle for the Clifford-Fourier transform
  publication-title: Adv. Appl. Clifford Algebras
  doi: 10.1007/s00006-022-01244-w
– volume: 2022
  issue: 1
  year: 2022
  ident: CR60
  article-title: On the class of uncertainty inequalities for the coupled fractional Fourier transform
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-022-02873-2
– volume: 285
  start-page: 1005
  issue: 6
  year: 2012
  end-page: 1009
  ident: CR56
  article-title: Color image encoding using fractional Fourier transformation associated with wavelet transformation
  publication-title: Opt. Commun.
  doi: 10.1016/j.optcom.2011.10.019
– volume: 89
  start-page: 339
  issue: 3
  year: 2009
  end-page: 343
  ident: CR26
  article-title: The logarithmic, Heisenberg’s and short-time uncertainty principles associated with fractional Fourier transform
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2008.09.002
– volume: 39
  issue: 4
  year: 2020
  ident: CR12
  article-title: Discrete octonion Fourier transform and the analysis of discrete 3-D data
  publication-title: Comput. Appl. Math.
  doi: 10.1007/s40314-020-01373-7
– year: 2006
  ident: CR59
  publication-title: Non-associative Algebra and Its Applications
  doi: 10.1201/9781420003451
– volume: 11
  issue: 5
  year: 2023
  ident: CR3
  article-title: Some essential relations for the quaternion quadratic-phase Fourier transform
  publication-title: Mathematics
  doi: 10.3390/math11051235
– ident: CR63
– volume: 40
  start-page: 3892
  issue: 11
  year: 2017
  end-page: 3900
  ident: CR38
  article-title: Uncertainty principle for measurable sets and signal recovery in quaternion domains
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.4271
– start-page: 191
  year: 2005
  end-page: 243
  ident: CR32
  article-title: Fourier uncertainty principles
  publication-title: Time-Frequency and Time-Scale Methods: Adaptive Decompositions, Uncertainty Principles, and Sampling
– start-page: 239
  year: 1999
  end-page: 291
  ident: CR52
  article-title: Introduction to the fractional Fourier transform and its applications
  publication-title: Advances in Imaging and Electron Physics
– volume: 33
  start-page: 389
  issue: 3
  year: 1991
  end-page: 404
  ident: CR6
  article-title: The fractional Fourier transform and applications
  publication-title: SIAM Rev.
  doi: 10.1137/1033097
– volume: 49
  start-page: 906
  issue: 3
  year: 1989
  end-page: 931
  ident: CR18
  article-title: Uncertainty principles and signal recovery
  publication-title: SIAM J. Appl. Math.
  doi: 10.1137/0149053
– year: 2015
  ident: CR31
  publication-title: Linear Canonical Transforms: Theory and Applications
– volume: 484
  issue: 2
  year: 2020
  ident: CR44
  article-title: Sharp inequalities for geometric Fourier transform and associated ambiguity function
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2019.123730
– volume: 11
  issue: 2
  year: 2023
  ident: CR49
  article-title: Integral equation via fixed point theorems on a new type of convex contraction in b-metric and 2-metric spaces
  publication-title: Mathematics
  doi: 10.3390/math11020344
– volume: 38
  start-page: 395
  issue: 1
  year: 2019
  end-page: 406
  ident: CR34
  article-title: Uncertainty principles for the offset linear canonical transform
  publication-title: Circuits Syst. Signal Process.
  doi: 10.1007/s00034-018-0863-z
– year: 1995
  ident: CR50
  publication-title: Introduction to Octonion and Other Non-associative Algebras in Physics
  doi: 10.1017/CBO9780511524479
– volume: 14
  start-page: 1
  issue: 3
  year: 2023
  end-page: 27
  ident: CR7
  article-title: Uncertainty inequalities for certain connected Lie groups
  publication-title: Ann. Funct. Anal.
  doi: 10.1007/s43034-023-00280-2
– volume: 29
  start-page: 1
  year: 2019
  end-page: 19
  ident: CR1
  article-title: Uncertainty principles for the quaternion linear canonical transform
  publication-title: Adv. Appl. Clifford Algebras
  doi: 10.1007/s00006-019-1020-x
– start-page: 521
  year: 2003
  ident: CR8
  article-title: Color image watermarking using quaternion Fourier transform
  publication-title: 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP’03)
– year: 1948
  ident: CR67
  publication-title: Introduction to the Theory of Fourier Integrals
– volume: 37
  start-page: 4155
  issue: 13
  year: 2023
  end-page: 4170
  ident: CR55
  article-title: An n-dimensional pseudo-differential operator involving linear canonical transform and some applications in quantum mechanics
  publication-title: Filomat
  doi: 10.2298/FIL2313155P
– volume: 136
  start-page: 29
  year: 2017
  end-page: 37
  ident: CR13
  article-title: Octonion Fourier transform of real-valued functions of three variables-selected properties and examples
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2016.11.021
– volume: 164
  start-page: 295
  year: 2019
  end-page: 300
  ident: CR43
  article-title: The octonionic Fourier transform: uncertainty relations and convolution
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2019.06.015
– volume: 3
  start-page: 239
  year: 2012
  end-page: 254
  ident: CR54
  article-title: Fractional Fourier transform of tempered distributions and generalized pseudo-differential operator
  publication-title: J. Pseudo-Differ. Oper. Appl.
  doi: 10.1007/s11868-012-0047-8
– volume: 44
  start-page: 257
  issue: 2
  year: 2024
  end-page: 264
  ident: CR73
  article-title: Uncertainty principles of fractional Fourier transform
  publication-title: Acta Math. Sci. Ser. A Chin. Ed.
– ident: CR28
– volume: 31
  start-page: 538
  issue: 7
  year: 2020
  end-page: 555
  ident: CR5
  article-title: Uncertainty principles for the continuous shearlet transforms in arbitrary space dimensions
  publication-title: Integral Transforms Spec. Funct.
  doi: 10.1080/10652469.2019.1707816
– volume: 10
  start-page: 1519
  year: 2016
  end-page: 1525
  ident: CR64
  article-title: Uncertainty principles for discrete signals associated with the fractional Fourier and linear canonical transforms
  publication-title: Signal Image Video Process.
  doi: 10.1007/s11760-016-0965-7
– volume: 12
  start-page: 1772
  issue: 8
  year: 1971
  end-page: 1780
  ident: CR48
  article-title: Linear canonical transformations and their unitary representations
  publication-title: J. Math. Phys.
  doi: 10.1063/1.1665805
– volume: 101
  year: 2022
  ident: 3213_CR42
  publication-title: Signal Process. Image Commun.
  doi: 10.1016/j.image.2021.116574
– volume: 6
  issue: 6
  year: 2020
  ident: 3213_CR39
  publication-title: Int. J. Appl. Comput. Math.
  doi: 10.1007/s40819-020-00917-z
– volume: 27
  start-page: 213
  issue: 3
  year: 2016
  ident: 3213_CR69
  publication-title: Integral Transforms Spec. Funct.
  doi: 10.1080/10652469.2015.1114482
– volume: 11
  issue: 19
  year: 2023
  ident: 3213_CR46
  publication-title: Mathematics
  doi: 10.3390/math11194101
– volume: 88
  start-page: 2511
  issue: 10
  year: 2008
  ident: 3213_CR25
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2008.04.012
– volume-title: Lectures on the Fourier Transform and Its Applications
  year: 2019
  ident: 3213_CR51
– volume: 2022
  issue: 1
  year: 2022
  ident: 3213_CR60
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-022-02873-2
– volume: 44
  start-page: 14236
  issue: 18
  year: 2021
  ident: 3213_CR74
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.7692
– volume: 11
  issue: 5
  year: 2023
  ident: 3213_CR3
  publication-title: Mathematics
  doi: 10.3390/math11051235
– volume: 44
  start-page: 257
  issue: 2
  year: 2024
  ident: 3213_CR73
  publication-title: Acta Math. Sci. Ser. A Chin. Ed.
– volume: 285
  start-page: 1005
  issue: 6
  year: 2012
  ident: 3213_CR56
  publication-title: Opt. Commun.
  doi: 10.1016/j.optcom.2011.10.019
– ident: 3213_CR63
  doi: 10.1002/mma.9440
– volume: 484
  issue: 2
  year: 2020
  ident: 3213_CR44
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2019.123730
– volume: 33
  start-page: 389
  issue: 3
  year: 1991
  ident: 3213_CR6
  publication-title: SIAM Rev.
  doi: 10.1137/1033097
– volume-title: Fourier Transforms
  year: 1995
  ident: 3213_CR65
– volume: 136
  start-page: 29
  year: 2017
  ident: 3213_CR13
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2016.11.021
– volume: 247
  start-page: 675
  year: 2014
  ident: 3213_CR36
  publication-title: Appl. Math. Comput.
– volume: 14
  start-page: 1
  issue: 3
  year: 2023
  ident: 3213_CR7
  publication-title: Ann. Funct. Anal.
  doi: 10.1007/s43034-023-00280-2
– volume: 11
  issue: 2
  year: 2023
  ident: 3213_CR49
  publication-title: Mathematics
  doi: 10.3390/math11020344
– volume: 31
  start-page: 538
  issue: 7
  year: 2020
  ident: 3213_CR5
  publication-title: Integral Transforms Spec. Funct.
  doi: 10.1080/10652469.2019.1707816
– ident: 3213_CR29
– volume-title: Linear Canonical Transforms: Theory and Applications
  year: 2015
  ident: 3213_CR31
– volume-title: The Geometry of the Octonions
  year: 2015
  ident: 3213_CR19
  doi: 10.1142/8456
– start-page: 191
  volume-title: Time-Frequency and Time-Scale Methods: Adaptive Decompositions, Uncertainty Principles, and Sampling
  year: 2005
  ident: 3213_CR32
– volume-title: Abstract and Applied Analysis
  year: 2013
  ident: 3213_CR37
– volume: 11
  issue: 3
  year: 2023
  ident: 3213_CR24
  publication-title: Mathematics
  doi: 10.3390/math11030677
– volume-title: The Uncertainty Principle in Harmonic Analysis
  year: 2012
  ident: 3213_CR30
– volume: 33
  issue: 1
  year: 2023
  ident: 3213_CR40
  publication-title: Adv. Appl. Clifford Algebras
  doi: 10.1007/s00006-022-01244-w
– volume: 11
  issue: 13
  year: 2023
  ident: 3213_CR11
  publication-title: Mathematics
  doi: 10.3390/math11133002
– volume-title: Non-associative Algebra and Its Applications
  year: 2006
  ident: 3213_CR59
  doi: 10.1201/9781420003451
– volume: 12
  start-page: 1772
  issue: 8
  year: 1971
  ident: 3213_CR48
  publication-title: J. Math. Phys.
  doi: 10.1063/1.1665805
– ident: 3213_CR70
  doi: 10.1002/mma.9126
– volume: 127
  start-page: 11657
  issue: 24
  year: 2016
  ident: 3213_CR58
  publication-title: Optik
  doi: 10.1016/j.ijleo.2016.09.069
– volume: 40
  start-page: 3892
  issue: 11
  year: 2017
  ident: 3213_CR38
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.4271
– volume: 434
  start-page: 1489
  issue: 2
  year: 2016
  ident: 3213_CR14
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2015.09.068
– ident: 3213_CR28
– volume: 42
  start-page: 466
  issue: 2
  year: 2019
  ident: 3213_CR35
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.5353
– volume-title: Introduction to Octonion and Other Non-associative Algebras in Physics
  year: 1995
  ident: 3213_CR50
  doi: 10.1017/CBO9780511524479
– volume: 44
  start-page: 10416
  issue: 13
  year: 2021
  ident: 3213_CR61
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.7417
– volume: 20
  issue: 4
  year: 2023
  ident: 3213_CR27
  publication-title: Mediterr. J. Math.
  doi: 10.1007/s00009-023-02403-4
– volume: 123
  start-page: 1897
  issue: 6
  year: 1995
  ident: 3213_CR9
  publication-title: Proc. Am. Math. Soc.
– volume: 15
  start-page: 1
  issue: 2
  year: 2024
  ident: 3213_CR22
  publication-title: J. Pseudo-Differ. Oper. Appl.
  doi: 10.1007/s11868-024-00590-6
– volume: 11
  issue: 5
  year: 2023
  ident: 3213_CR45
  publication-title: Mathematics
  doi: 10.3390/math11051158
– volume: 4
  year: 2023
  ident: 3213_CR10
  publication-title: e-Prime-Adv. Electr. Eng. Electron. Energy
  doi: 10.1016/j.prime.2023.100162
– volume: 10
  start-page: 1519
  year: 2016
  ident: 3213_CR64
  publication-title: Signal Image Video Process.
  doi: 10.1007/s11760-016-0965-7
– volume-title: Quaternion Fourier Transforms for Signal and Image Processing
  year: 2014
  ident: 3213_CR20
  doi: 10.1002/9781118930908
– volume: 38
  start-page: 395
  issue: 1
  year: 2019
  ident: 3213_CR34
  publication-title: Circuits Syst. Signal Process.
  doi: 10.1007/s00034-018-0863-z
– volume: 39
  issue: 4
  year: 2020
  ident: 3213_CR12
  publication-title: Comput. Appl. Math.
  doi: 10.1007/s40314-020-01373-7
– volume: 29
  start-page: 595
  issue: 4
  year: 2022
  ident: 3213_CR62
  publication-title: Georgian Math. J.
  doi: 10.1515/gmj-2022-2158
– volume: 43
  start-page: 1953
  issue: 4
  year: 2020
  ident: 3213_CR57
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.6018
– start-page: 521
  volume-title: 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP’03)
  year: 2003
  ident: 3213_CR8
– volume: 188
  year: 2021
  ident: 3213_CR23
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2021.108233
– volume-title: The Fractional Fourier Transform with Applications in Optics and Signal Processing
  year: 2001
  ident: 3213_CR53
– volume: 37
  start-page: 4155
  issue: 13
  year: 2023
  ident: 3213_CR55
  publication-title: Filomat
  doi: 10.2298/FIL2313155P
– volume: 12
  start-page: 2238
  issue: 12
  year: 2018
  ident: 3213_CR15
  publication-title: IET Image Process.
  doi: 10.1049/iet-ipr.2018.5440
– volume: 29
  start-page: 1
  year: 2019
  ident: 3213_CR1
  publication-title: Adv. Appl. Clifford Algebras
  doi: 10.1007/s00006-019-1020-x
– volume: 3
  start-page: 207
  year: 1997
  ident: 3213_CR21
  publication-title: J. Fourier Anal. Appl.
  doi: 10.1007/BF02649110
– volume: 25
  start-page: 647
  issue: 3
  year: 2008
  ident: 3213_CR66
  publication-title: J. Opt. Soc. Am. A
  doi: 10.1364/JOSAA.25.000647
– volume-title: Abstract and Applied Analysis
  year: 2016
  ident: 3213_CR4
– volume: 29
  start-page: 237
  issue: 1–2
  year: 1991
  ident: 3213_CR33
  publication-title: Ark. Mat.
  doi: 10.1007/BF02384339
– start-page: 239
  volume-title: Advances in Imaging and Electron Physics
  year: 1999
  ident: 3213_CR52
– volume: 423
  start-page: 681
  issue: 1
  year: 2015
  ident: 3213_CR16
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2014.10.003
– volume: 89
  start-page: 339
  issue: 3
  year: 2009
  ident: 3213_CR26
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2008.09.002
– ident: 3213_CR2
– volume: 3
  start-page: 239
  year: 2012
  ident: 3213_CR54
  publication-title: J. Pseudo-Differ. Oper. Appl.
  doi: 10.1007/s11868-012-0047-8
– volume: 2012
  start-page: 1
  year: 2012
  ident: 3213_CR41
  publication-title: EURASIP J. Adv. Signal Process.
  doi: 10.1186/1687-6180-2012-120
– volume: 46
  start-page: 2651
  issue: 2
  year: 2023
  ident: 3213_CR71
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.8667
– volume-title: On Quaternions and Octonions
  year: 2003
  ident: 3213_CR17
  doi: 10.1201/9781439864180
– volume: 49
  start-page: 906
  issue: 3
  year: 1989
  ident: 3213_CR18
  publication-title: SIAM J. Appl. Math.
  doi: 10.1137/0149053
– volume: 16
  start-page: 853
  issue: 10
  year: 2009
  ident: 3213_CR68
  publication-title: IEEE Signal Process. Lett.
  doi: 10.1109/LSP.2009.2026107
– volume: 11
  issue: 12
  year: 2023
  ident: 3213_CR47
  publication-title: Mathematics
  doi: 10.3390/math11122742
– volume-title: Introduction to the Theory of Fourier Integrals
  year: 1948
  ident: 3213_CR67
– volume: 164
  start-page: 295
  year: 2019
  ident: 3213_CR43
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2019.06.015
– volume: 28
  start-page: 1
  year: 2018
  ident: 3213_CR72
  publication-title: Adv. Appl. Clifford Algebras
  doi: 10.1007/s00006-018-0828-0
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Snippet In this article, we define the octonion quadratic-phase Fourier transform (OQPFT) and derive its inversion formula, including its fundamental properties such...
Abstract In this article, we define the octonion quadratic-phase Fourier transform (OQPFT) and derive its inversion formula, including its fundamental...
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SubjectTerms Algebra
Analysis
Applications of Mathematics
Data compression
Fourier transform
Fourier transforms
Inequalities
Inequality
Integral transforms
Investigations
Lie groups
Mathematics
Mathematics and Statistics
Octonion quadratic-phase Fourier transform
Principles
Quaternions
Sharp inequalities
Signal processing
Uncertainty principles
Wavelet transforms
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Title Octonion quadratic-phase Fourier transform: inequalities, uncertainty principles, and examples
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