Mathematical analysis research group
TalTech priority area
Research classification (Frascati)
Head of the research group
Research group member
Doctoral students
Keyword
Overview
The main directions of research are as follows: Studying the generalized Shannon sampling operators that mean the representations of functions in terms of series, wherethe expansion coefficients are its samplesand expansion functions are translatesof certain kernel function. In the case ofKantorovich-type sampling operators wetake, instead of point estimates, some localaverages as Fejer-type singular integrals. Studying sampling operators, definedusing cosine operator framework, their approximation properties and possibleapplications. Studying applications of the generalizedsampling operators in Signal Processing,especially in imaging applications, wherethe generalized sampling operators area natural tool for image resampling. Wealso study applications in HDR imaging.We study the applications of sampling operators in time series analysis and linearprediction. Studying representations of the derivatives (also fractional derivatives) withKantorovich-type sampling operators.We study sampling in fractional Fourierframework. Studying possibilities of applying ourapproximation-theoretic results in deeplearning.
Important results
Main results: We studied sampling operators for one-bitsampling. We studied Kantorovich-type samplingoperators for derivative sampling. We defined a family of fractional derivativemasks for image processing. We studied approximation properties ofsampling operators, defined using cosineoperator framework.
Related projects
Related department
- Martens, O., Metshein, M., Tamberg, G., Abdullayev, A. Impedance cardiography signal processing with Savitzky-Golay and frequency sampling kernels // 2022 18th Biennial Baltic Electronics Conference (BEC). : IEEE, 2022. 5 l..
https://doi.org/10.1109/BEC56180.2022.9935597 - Rassõlkin, A., Vaimann, T., Org, P., Leibak, A., Gordon, R., Priidel, E. ADCS development for student CubeSat satellites - TalTech case study // Proceedings of the Estonian Academy of Sciences (2021) 3, p. 268-285 : ill.
https://doi.org/10.3176/proc.2021.3.06 - Leibak, A. Michailichenko group of matrices over skew-fields // Математицки весник = Matematički Vesnik (2019) vol. 71 , 1-2, p. 155–161.
http://www.vesnik.math.rs/vol/mv191210.pdf - Graf, O., Tamberg, G. On some norms and approximation properties of Kantorovich-type sampling operators // 2019 International Conference on Sampling Theory and Applications (SampTA) : 13th International Conference : Bordeaux, France, July 8-12, 2019 : [proceedings]. [S.l.] : IEEE Computer Society Press, 2019. 4 p.
https://sampta2019.sciencesconf.org/browse/author?authorid=715157 - Saksa, A., Kivinukk, A., Graf, O. On the cosine operator function framework of windowed Shannon sampling operators // 2019 International Conference on Sampling Theory and Applications (SampTA) : 13th International Conference : Bordeaux, France, July 8-12, 2019 : [proceedings]. [S.l.] : IEEE Computer Society Press, 2019. 4 p.
https://sampta2019.sciencesconf.org/browse/author?authorid=715157 - Graf, O., Krahmer, F., Krause-Solberg, S. Higher order 1-bit Sigma-Delta modulation on a circle // 2019 International Conference on Sampling Theory and Applications (SampTA) : 13th International Conference : Bordeaux, France, July 8-12, 2019 : [proceedings]. [S.l.] : IEEE Computer Society Press, 2019. 5 p.
https://sampta2019.sciencesconf.org/browse/author?authorid=715157 - Kotta, Ü., Belikov, J., Halas, M., Leibak, A. Degree of Dieudonne determinant defines the order of nonlinear system // International journal of control (2019) vol. 92, 3, p. 518-527.
https://doi.org/10.1080/00207179.2017.1361042 - Ahmed, F., Kervadec, C., Le Moullec, Y., Tamberg, G., Annus, P. Autonomous wireless sensor networks : implementation of transient computing and energy prediction for improved node performance and link quality // The Computer Journal (2019) vol. 62, 6, p. 820 - 837.
https://doi.org/10.1093/comjnl/bxy101 - Ahmed, F., Tamberg, G., Le Moullec, Y., Annus, P. Adaptive LINE-P : an adaptive linear energy prediction model for wireless sensor network nodes // Sensors (2018) vol. 18, 4, art. 1105, 26 p. : ill.
https://doi.org/10.3390/s18041105 - Kivinukk, A., Tamberg, G. On generalized Shannon sampling operators in the cosine operator function framework // Sampling, approximation, and signal analysis : harmonic analysis in the spirit of J. Rowland Higgins. : Birkhäuser Cham, 2023. p. 39-68. (Applied and numerical harmonic analysis).
https://doi.org/10.1007/978-3-031-41130-4_3 - Leibak, A. On the number of factorizations of t mod N and the probability distribution of Diffie-Hellman secret keys for many users // Advances in mathematics of communications (2023) vol. 17, 4, p. 920-927.
https://doi.org/10.3934/amc.2021029 - Kivinukk, A., Tamberg, G. A note on the cosine operator function for Mellin sampling series // Sampling theory signal processing and data analysis (2024) vol. 22, 1, 16 p.
https://doi.org/10.1007/s43670-023-00081-7