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Effective numerical evaluation of the double Hilbert transform
- Source :
- Mathematical Methods in the Applied Sciences.
- Publication Year :
- 2020
- Publisher :
- Wiley, 2020.
-
Abstract
- In this paper, we propose two methods to compute the double Hilbert transform of periodic functions. First, we establish the quadratic formula of trigonometric interpolation type for double Hilbert transform and obtain an estimation of the remainder. We call this method 2D mechanical quadrature method (2D-MQM). Numerical experiments show that 2D-MQM outperforms the library function “hilbert” in Matlab when the values of the functions being handled are very large or approach to infinity. Second, we propose a complex analytic method to calculate the double Hilbert transform, which is based on the 2D adaptive Fourier decomposition, and the method is called as 2D-HAFD. In contrast to the pointwise approximation, 2D-HAFD provides explicit rational functional approximations and is valid for all signals of finite energy.
- Subjects :
- Pointwise
General Mathematics
010102 general mathematics
General Engineering
01 natural sciences
010101 applied mathematics
Periodic function
Quadratic formula
symbols.namesake
symbols
Applied mathematics
Nyström method
Hilbert transform
0101 mathematics
Remainder
Energy (signal processing)
Mathematics
Trigonometric interpolation
Subjects
Details
- ISSN :
- 10991476 and 01704214
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi...........b18c22aa5e9e4702adb46c917c3741b8