Mai, Weixiong; Qian, Tao Algorithm of adaptive Fourier decomposition in \(H^2(\mathbb{C}^+)\). (English) Zbl 1521.94013 Int. J. Wavelets Multiresolut. Inf. Process. 21, No. 5, Article ID 2350011, 10 p. (2023). MSC: 94A12 42A38 93B11 PDFBibTeX XMLCite \textit{W. Mai} and \textit{T. Qian}, Int. J. Wavelets Multiresolut. Inf. Process. 21, No. 5, Article ID 2350011, 10 p. (2023; Zbl 1521.94013) Full Text: DOI
Qian, Tao Sparse representations of random signals. (English) Zbl 07780822 Math. Methods Appl. Sci. 45, No. 8, 4210-4230 (2022). MSC: 94A12 42A16 42A20 41A30 30B99 35A35 PDFBibTeX XMLCite \textit{T. Qian}, Math. Methods Appl. Sci. 45, No. 8, 4210--4230 (2022; Zbl 07780822) Full Text: DOI
Qian, Tao Positive-instantaneous frequency and approximation. (English) Zbl 1492.94036 Front. Math. China 17, No. 3, 337-371 (2022); translation from Adv. Math., Beijing 47, No. 3, 321–347 (2018). MSC: 94A12 42A50 30H10 30J05 30J10 32A50 PDFBibTeX XMLCite \textit{T. Qian}, Front. Math. China 17, No. 3, 337--371 (2022; Zbl 1492.94036); translation from Adv. Math., Beijing 47, No. 3, 321--347 (2018) Full Text: DOI
Mi, Wen; Qian, Tao System identification of Hammerstein models by using backward shift algorithm. (English) Zbl 1510.93336 Appl. Math. Comput. 413, Article ID 126620, 11 p. (2022). MSC: 93E12 42A38 62M15 94A12 PDFBibTeX XMLCite \textit{W. Mi} and \textit{T. Qian}, Appl. Math. Comput. 413, Article ID 126620, 11 p. (2022; Zbl 1510.93336) Full Text: DOI
Qu, Wei; Qian, Tao; Deng, Guan-Tie A stochastic sparse representation: \(n\)-best approximation to random signals and computation. (English) Zbl 1471.94012 Appl. Comput. Harmon. Anal. 55, 185-198 (2021). MSC: 94A12 41A30 41A50 30B99 60G35 60G07 60G10 94A08 PDFBibTeX XMLCite \textit{W. Qu} et al., Appl. Comput. Harmon. Anal. 55, 185--198 (2021; Zbl 1471.94012) Full Text: DOI
Chen, Qiuhui; Li, Luoqing; Qian, Tao Time-frequency transform involving nonlinear modulation and frequency-varying dilation. (English) Zbl 1460.42007 Complex Var. Elliptic Equ. 65, No. 11, 1800-1813 (2020). MSC: 42A38 42C15 44A15 62P30 94A20 PDFBibTeX XMLCite \textit{Q. Chen} et al., Complex Var. Elliptic Equ. 65, No. 11, 1800--1813 (2020; Zbl 1460.42007) Full Text: DOI
Chen, Qiuhui; Qian, Tao; Tan, Lihui A theory on non-constant frequency decompositions and applications. (English) Zbl 1494.94015 Breaz, Daniel (ed.) et al., Advancements in complex analysis. From theory to practice. Cham: Springer. 1-37 (2020). MSC: 94A12 30H10 41A20 94-02 PDFBibTeX XMLCite \textit{Q. Chen} et al., in: Advancements in complex analysis. From theory to practice. Cham: Springer. 1--37 (2020; Zbl 1494.94015) Full Text: DOI
Chen, Qiuhui; Dang, Pei; Qian, Tao Spectra of rational orthonormal systems. (English) Zbl 1429.42005 Sci. China, Math. 62, No. 10, 1961-1976 (2019). Reviewer: Yamilet del Carmen Quintana Mato (Caracas) MSC: 42A38 44A15 62P30 94A20 42C05 33C45 PDFBibTeX XMLCite \textit{Q. Chen} et al., Sci. China, Math. 62, No. 10, 1961--1976 (2019; Zbl 1429.42005) Full Text: DOI
Li, Yanting; Zhang, Liming; Qian, Tao 2D partial unwinding – a novel non-linear phase decomposition of images. (English) Zbl 07123013 IEEE Trans. Image Process. 28, No. 10, 4762-4773 (2019). MSC: 94-XX PDFBibTeX XMLCite \textit{Y. Li} et al., IEEE Trans. Image Process. 28, No. 10, 4762--4773 (2019; Zbl 07123013) Full Text: DOI
Qian, Tao; Tan, Lihui Characterizations of mono-components: the Blaschke and starlike types. (English) Zbl 1491.30007 Complex Anal. Oper. Theory 12, No. 6, 1383-1399 (2018). MSC: 30C45 94A12 30H10 44A15 PDFBibTeX XMLCite \textit{T. Qian} and \textit{L. Tan}, Complex Anal. Oper. Theory 12, No. 6, 1383--1399 (2018; Zbl 1491.30007) Full Text: DOI
Gao, You; Ku, Min; Qian, Tao Fast algorithm of adaptive Fourier series. (English) Zbl 1440.42023 Math. Methods Appl. Sci. 41, No. 7, 2654-2663 (2018). MSC: 42A50 32A30 32A35 46J15 94A12 PDFBibTeX XMLCite \textit{Y. Gao} et al., Math. Methods Appl. Sci. 41, No. 7, 2654--2663 (2018; Zbl 1440.42023) Full Text: DOI arXiv
Li, Youfa; Qian, Tao Reconstruction of analytic signal in Sobolev space by framelet sampling approximation. (English) Zbl 1387.42045 Appl. Anal. 97, No. 2, 194-209 (2018). MSC: 42C40 65T60 94A20 PDFBibTeX XMLCite \textit{Y. Li} and \textit{T. Qian}, Appl. Anal. 97, No. 2, 194--209 (2018; Zbl 1387.42045) Full Text: DOI
Tan, LiHui; Qian, Tao Extracting outer function part from Hardy space function. (English) Zbl 1395.30055 Sci. China, Math. 60, No. 11, 2321-2336 (2017). MSC: 30H10 30J05 30J10 94A12 PDFBibTeX XMLCite \textit{L. Tan} and \textit{T. Qian}, Sci. China, Math. 60, No. 11, 2321--2336 (2017; Zbl 1395.30055) Full Text: DOI
Dang, Pei; Qian, Tao; Chen, Qiuhui Uncertainty principle and phase-amplitude analysis of signals on the unit sphere. (English) Zbl 1386.94025 Adv. Appl. Clifford Algebr. 27, No. 4, 2985-3013 (2017). MSC: 94A12 PDFBibTeX XMLCite \textit{P. Dang} et al., Adv. Appl. Clifford Algebr. 27, No. 4, 2985--3013 (2017; Zbl 1386.94025) Full Text: DOI
Zhang, Liming; Qian, Tao; Mai, Weixiong; Dang, Pei Adaptive Fourier decomposition-based Dirac type time-frequency distribution. (English) Zbl 1369.94331 Math. Methods Appl. Sci. 40, No. 8, 2815-2833 (2017). MSC: 94A12 42A50 PDFBibTeX XMLCite \textit{L. Zhang} et al., Math. Methods Appl. Sci. 40, No. 8, 2815--2833 (2017; Zbl 1369.94331) Full Text: DOI
Chen, Qiuhui; Dang, Pei; Qian, Tao A frame theory of Hardy spaces with the quaternionic and the Clifford algebra settings. (English) Zbl 1376.42009 Adv. Appl. Clifford Algebr. 27, No. 2, 1073-1101 (2017). MSC: 42A38 44A15 62P30 94A20 PDFBibTeX XMLCite \textit{Q. Chen} et al., Adv. Appl. Clifford Algebr. 27, No. 2, 1073--1101 (2017; Zbl 1376.42009) Full Text: DOI
Yang, Yan; Dang, Pei; Qian, Tao Tighter uncertainty principles based on quaternion Fourier transform. (English) Zbl 1338.42013 Adv. Appl. Clifford Algebr. 26, No. 1, 479-497 (2016). MSC: 42B10 46F10 30G35 94A12 PDFBibTeX XMLCite \textit{Y. Yang} et al., Adv. Appl. Clifford Algebr. 26, No. 1, 479--497 (2016; Zbl 1338.42013) Full Text: DOI
Dang, Pei; Qian, Tao; Yang, Yan Extra-strong uncertainty principles in relation to phase derivative for signals in Euclidean spaces. (English) Zbl 1366.94092 J. Math. Anal. Appl. 437, No. 2, 912-940 (2016). MSC: 94A12 30G35 42B37 PDFBibTeX XMLCite \textit{P. Dang} et al., J. Math. Anal. Appl. 437, No. 2, 912--940 (2016; Zbl 1366.94092) Full Text: DOI
Tan, Lihui; Qian, Tao; Chen, Qiuhui New aspects of Beurling-Lax shift invariant subspaces. (English) Zbl 1338.94021 Appl. Math. Comput. 256, 257-266 (2015). MSC: 94A12 42A38 PDFBibTeX XMLCite \textit{L. Tan} et al., Appl. Math. Comput. 256, 257--266 (2015; Zbl 1338.94021) Full Text: DOI
Li, Youfa; Chen, Qiuhui; Qian, Tao; Wang, Yi Sampling error analysis and some properties of non-bandlimited signals that are reconstructed by generalized sinc functions. (English) Zbl 1290.94024 Appl. Anal. 93, No. 2, 305-315 (2014). MSC: 94A20 PDFBibTeX XMLCite \textit{Y. Li} et al., Appl. Anal. 93, No. 2, 305--315 (2014; Zbl 1290.94024) Full Text: DOI arXiv
Dang, Pei; Deng, Guan-Tie; Qian, Tao A tighter uncertainty principle for linear canonical transform in terms of phase derivative. (English) Zbl 1393.94205 IEEE Trans. Signal Process. 61, No. 21, 5153-5164 (2013). MSC: 94A12 PDFBibTeX XMLCite \textit{P. Dang} et al., IEEE Trans. Signal Process. 61, No. 21, 5153--5164 (2013; Zbl 1393.94205) Full Text: DOI
Chen, Qiuhui; Qian, Tao; Li, Youfa Shannon-type sampling for multivariate non-bandlimited signals. (English) Zbl 1283.94030 Sci. China, Math. 56, No. 9, 1915-1934 (2013). MSC: 94A20 42A38 44A15 PDFBibTeX XMLCite \textit{Q. Chen} et al., Sci. China, Math. 56, No. 9, 1915--1934 (2013; Zbl 1283.94030) Full Text: DOI
Li, Youfa; Qian, Tao Analytic sampling approximation by projection operator with application in decomposition of instantaneous frequency. (English) Zbl 1279.41020 Int. J. Wavelets Multiresolut. Inf. Process. 11, No. 5, Article ID 1350040, 19 p. (2013). MSC: 41A20 41A25 94A20 PDFBibTeX XMLCite \textit{Y. Li} and \textit{T. Qian}, Int. J. Wavelets Multiresolut. Inf. Process. 11, No. 5, Article ID 1350040, 19 p. (2013; Zbl 1279.41020) Full Text: DOI
Dang, Pei; Qian, Tao; Guo, Yuan Yuan Transient time-frequency distribution based on mono-component decompositions. (English) Zbl 1316.94025 Int. J. Wavelets Multiresolut. Inf. Process. 11, No. 3, Article ID 1350022, 24 p. (2013). MSC: 94A12 42A38 PDFBibTeX XMLCite \textit{P. Dang} et al., Int. J. Wavelets Multiresolut. Inf. Process. 11, No. 3, Article ID 1350022, 24 p. (2013; Zbl 1316.94025) Full Text: DOI
Qian, Tao; Li, Hong; Stessin, Michael Comparison of adaptive mono-component decompositions. (English) Zbl 1270.94041 Nonlinear Anal., Real World Appl. 14, No. 2, 1055-1074 (2013). MSC: 94A12 42A10 65T50 PDFBibTeX XMLCite \textit{T. Qian} et al., Nonlinear Anal., Real World Appl. 14, No. 2, 1055--1074 (2013; Zbl 1270.94041) Full Text: DOI
Deng, Guan-Tie; Qian, Tao An application of entire function theory to analytic signals. (English) Zbl 1242.94007 J. Math. Anal. Appl. 389, No. 1, 54-57 (2012). MSC: 94A12 30D20 30H10 PDFBibTeX XMLCite \textit{G.-T. Deng} and \textit{T. Qian}, J. Math. Anal. Appl. 389, No. 1, 54--57 (2012; Zbl 1242.94007) Full Text: DOI
Qian, Tao; Zhang, Liming; Li, Zhixiong Algorithm of adaptive Fourier decomposition. (English) Zbl 1393.94142 IEEE Trans. Signal Process. 59, No. 12, 5899-5906 (2011). MSC: 94A11 94A12 42A16 PDFBibTeX XMLCite \textit{T. Qian} et al., IEEE Trans. Signal Process. 59, No. 12, 5899--5906 (2011; Zbl 1393.94142) Full Text: DOI
Dang, Pei; Qian, Tao Analytic phase derivatives, all-pass filters and signals of minimum phase. (English) Zbl 1392.94170 IEEE Trans. Signal Process. 59, No. 10, 4708-4718 (2011). MSC: 94A12 30E20 30H10 30J05 30J10 PDFBibTeX XMLCite \textit{P. Dang} and \textit{T. Qian}, IEEE Trans. Signal Process. 59, No. 10, 4708--4718 (2011; Zbl 1392.94170) Full Text: DOI
Qian, Tao; Wang, Rui; Xu, Yuesheng; Zhang, Haizhang Orthonormal bases with nonlinear phases. (English) Zbl 1213.42126 Adv. Comput. Math. 33, No. 1, 75-95 (2010). MSC: 42C30 94A12 PDFBibTeX XMLCite \textit{T. Qian} et al., Adv. Comput. Math. 33, No. 1, 75--95 (2010; Zbl 1213.42126) Full Text: DOI
Qian, Tao; Ho, I. T.; Leong, I. T.; Wang, Yanbo Adaptive decomposition of functions into pieces of non-negative instantaneous frequencies. (English) Zbl 1200.94026 Int. J. Wavelets Multiresolut. Inf. Process. 8, No. 5, 813-833 (2010). MSC: 94A12 94A11 42A50 PDFBibTeX XMLCite \textit{T. Qian} et al., Int. J. Wavelets Multiresolut. Inf. Process. 8, No. 5, 813--833 (2010; Zbl 1200.94026) Full Text: DOI
Chen, Qiuhui; Qian, Tao Sampling theorem and multi-scale spectrum based on non-linear Fourier atoms. (English) Zbl 1171.94331 Appl. Anal. 88, No. 6, 903-919 (2009). MSC: 94A20 PDFBibTeX XMLCite \textit{Q. Chen} and \textit{T. Qian}, Appl. Anal. 88, No. 6, 903--919 (2009; Zbl 1171.94331) Full Text: DOI
Qian, Tao; Zhang, Liming; Li, Hong Mono-components vs IMFs in signal decomposition. (English) Zbl 1145.94374 Int. J. Wavelets Multiresolut. Inf. Process. 6, No. 3, 353-374 (2008). MSC: 94A12 30D55 31A20 31C05 42A50 42C15 44A15 PDFBibTeX XMLCite \textit{T. Qian} et al., Int. J. Wavelets Multiresolut. Inf. Process. 6, No. 3, 353--374 (2008; Zbl 1145.94374) Full Text: DOI
Kou, Kit Ian; Qian, Tao; Sommen, Frank Sampling with Bessel functions. (English) Zbl 1209.94029 Adv. Appl. Clifford Algebr. 17, No. 3, 519-536 (2007). MSC: 94A20 30G35 33C10 42A38 PDFBibTeX XMLCite \textit{K. I. Kou} et al., Adv. Appl. Clifford Algebr. 17, No. 3, 519--536 (2007; Zbl 1209.94029) Full Text: DOI
Qian, Tao Mono-components for signal decomposition. (English) Zbl 1110.94012 Tao, Qian (ed.) et al., Wavelet analysis and applications. Selected papers based on the presentations at the conference (WAA 2005), Macau, China, 29th November – 2nd December 2005. With CD-ROM. Basel: Birkhäuser (ISBN 3-7643-7777-1/hbk). Applied and Numerical Harmonic Analysis, 299-319 (2007). MSC: 94A12 30D55 31A20 31C05 42A50 42B20 PDFBibTeX XMLCite \textit{T. Qian}, in: Wavelet analysis and applications. Selected papers based on the presentations at the conference (WAA 2005), Macau, China, 29th November -- 2nd December 2005. With CD-ROM. Basel: Birkhäuser. 299--319 (2007; Zbl 1110.94012)
Chen, Qiuhui; Li, Luoqing; Qian, Tao Time-frequency aspects of nonlinear Fourier atoms. (English) Zbl 1138.94319 Tao, Qian (ed.) et al., Wavelet analysis and applications. Selected papers based on the presentations at the conference (WAA 2005), Macau, China, 29th November – 2nd December 2005. With CD-ROM. Basel: Birkhäuser (ISBN 3-7643-7777-1/hbk). Applied and Numerical Harmonic Analysis, 287-297 (2007). MSC: 94A12 42C15 94A20 PDFBibTeX XMLCite \textit{Q. Chen} et al., in: Wavelet analysis and applications. Selected papers based on the presentations at the conference (WAA 2005), Macau, China, 29th November -- 2nd December 2005. With CD-ROM. Basel: Birkhäuser. 287--297 (2007; Zbl 1138.94319)
Yang, Yan; Qian, Tao Co-dimension-\(p\) Shannon sampling theorems. (English) Zbl 1134.94003 Complex Var. Elliptic Equ. 52, No. 1, 9-20 (2007). Reviewer: Joseph Lakey (Las Cruces) MSC: 94A20 30G35 30D10 42B35 PDFBibTeX XMLCite \textit{Y. Yang} and \textit{T. Qian}, Complex Var. Elliptic Equ. 52, No. 1, 9--20 (2007; Zbl 1134.94003) Full Text: DOI
Qian, Tao; Chen, Qiuhui Characterization of analytic phase signals. (English) Zbl 1138.94007 Comput. Math. Appl. 51, No. 9-10, 1471-1482 (2006). MSC: 94A12 44A15 PDFBibTeX XMLCite \textit{T. Qian} and \textit{Q. Chen}, Comput. Math. Appl. 51, No. 9--10, 1471--1482 (2006; Zbl 1138.94007) Full Text: DOI
Chen, Qiuhui; Li, Luoqing; Qian, Tao Two families of unit analytic signals with nonlinear phase. (English) Zbl 1104.94004 Physica D 221, No. 1, 1-12 (2006). MSC: 94A12 44A15 PDFBibTeX XMLCite \textit{Q. Chen} et al., Physica D 221, No. 1, 1--12 (2006; Zbl 1104.94004) Full Text: DOI
Qian, Tao Mono-components for decomposition of signals. (English) Zbl 1104.94005 Math. Methods Appl. Sci. 29, No. 10, 1187-1198 (2006). MSC: 94A12 44A15 31A20 47A75 30C45 PDFBibTeX XMLCite \textit{T. Qian}, Math. Methods Appl. Sci. 29, No. 10, 1187--1198 (2006; Zbl 1104.94005) Full Text: DOI
Kou, Kit-Ian; Qian, Tao Shannon sampling in the Clifford analysis setting. (English) Zbl 1092.94019 Z. Anal. Anwend. 24, No. 4, 853-870 (2006). MSC: 94A20 41A05 PDFBibTeX XMLCite \textit{K.-I. Kou} and \textit{T. Qian}, Z. Anal. Anwend. 24, No. 4, 853--870 (2006; Zbl 1092.94019) Full Text: DOI
Qian, Tao Analytic signals and harmonic measures. (English) Zbl 1082.94006 J. Math. Anal. Appl. 314, No. 2, 526-536 (2006). Reviewer: Arjun K. Gupta (Bowling Green) MSC: 94A12 42B35 PDFBibTeX XMLCite \textit{T. Qian}, J. Math. Anal. Appl. 314, No. 2, 526--536 (2006; Zbl 1082.94006) Full Text: DOI
Qian, Tao; Chen, Qiuhui; Li, Luoqing Analytic unit quadrature signals with nonlinear phase. (English) Zbl 1070.94504 Physica D 203, No. 1-2, 80-87 (2005). MSC: 94A12 62M15 44A15 PDFBibTeX XMLCite \textit{T. Qian} et al., Physica D 203, No. 1--2, 80--87 (2005; Zbl 1070.94504) Full Text: DOI
Qian, Tao Paley-Wiener theorems and Shannon sampling in the Clifford analysis setting. (English) Zbl 1103.94012 Abłamowicz, Rafał (ed.), Clifford algebras. Applications to mathematics, physics, and engineering. Papers from the 6th international conference on Clifford algebras and their applications in mathematical physics, Cookeville, TN, USA, May 20–25, 2002. Boston, MA: Birkhäuser (ISBN 0-8176-3525-4/hbk). Progress in Mathematical Physics 34, 115-124 (2004). MSC: 94A20 41A05 30D15 15A66 PDFBibTeX XMLCite \textit{T. Qian}, Prog. Math. Phys. 34, 115--124 (2004; Zbl 1103.94012)