DEVELOPMENT OF MULTIDIMENSIONAL SIGNAL PROCESSING ALGORITHMS AND METHODS BASED ON BASIS FUNCTIONS
Keywords:
The advantage of the theory of spline functions with one variable is the good convergence of splines to approximated objects and the simplicity of the implementation of algorithms for constructing splines on a computerAbstract
Multidimensional signal processing algorithms and methods based on basis functions involve decomposing a signal into a set of basis functions that form a complete representation of the signal. This response provides an overview of the development of multidimensional signal processing algorithms and methods based on basis functions. The process involves selecting a set of orthogonal or linearly independent basis functions, representing the signal as a linear combination of these basis functions, applying signal analysis and processing techniques, and optimizing the algorithms for efficiency. This area of research has important applications in fields such as image and video processing, signal compression, and machine learning.
References
Chao Zeng, Fang Deng, Xin Li, and Jiansong Deng. Dimensions of biquadratic and bicubic spline spaces over hierarchical T-meshes. Journal of Computational and Applied Mathematics, 287:162–178, 2015.
Xilian Fu. A rational bicubic spline for visualization of shaped data. Journal of Computational Analysis and Applications, page 1532, 2018.
R Akhrif, A Kouibia, and M Pasadas. Approximation of generalized offset surfaces by bicubic splines. Journal of Mathematical Chemistry, 58(3):647–662, 2020.
A Kouibia and Miguel Pasadas. Approximation of surfaces by fairness bicubic splines. Advances in Computational Mathematics, 20(1-3):87–103, 2004.
Aleksandr Vasil’evich Mironenko. Uniform approximation by perfect splines. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 23(3):206–213, 2017.
A K B Chand and M A Navascués. Natural bicubic spline fractal interpolation. Nonlinear Analysis: Theory, Methods & Applications, 69(11):3679–3691, 2008.
Kh E Khujamatov, D T Khasanov, and E N Reypnazarov. Research and Modelling Adaptive Management of Hybrid Power Supply Systems for Object Telecommunications based on IoT. In 2019 International
Conference on Information Science and Communications Technologies (ICISCT), pages 1–5. IEEE, 2019.
Zumrad, I., & Feruza, A. (2022). LINGUISTICS, ITS MODERN TYPES. Journal of Modern Educational Achievements, 3, 43-47.
Kurbanova, M., Ibragimova, Z., & Nuriddinova, S. (2022). Lexico-Semantical Properties of Omonym and Alliance Words Used in Epics of Independence Periods. Periodica Journal of Modern Philosophy, Social Sciences and Humanities, 3, 93-96.
Omonovna, K. M., & Tolipovna, I. Z. (2021). The Problem of Traditions in the Works of Sergey Esenin. International Journal of Human Computing Studies, 3(1), 131-133.
Ибрагимова, З. (2022). ПОЛИСЕМАНТИК ЛЕКСЕМАЛАР. O'ZBEKISTONDA FANLARARO INNOVATSIYALAR VA ILMIY TADQIQOTLAR JURNALI, 2(13), 616-619.
