How to expand the Gaussian Kernel into series of eigenfunctions?
3 visualizaciones (últimos 30 días)
Mostrar comentarios más antiguos
saadi
el 24 de Dic. de 2019
Comentada: Vladimir Sovkov
el 24 de Dic. de 2019
I have a gaussian kernal
How to expand it into a series of eigenfunctions ?Any help will be appreciated.
0 comentarios
Respuesta aceptada
Vladimir Sovkov
el 24 de Dic. de 2019
Fitst of all, you should specify --nothing can be done with an arbtrary function. Then, you can try to calculate the integrals analytically using the call function "int" in the Symbolic Math Toolbox, but there is no guarantee that an analytical solution exists at all. To find the numerical solution you should compute the integrals numerically at every x, y, i of interest; use the call function "inegral" for this purpose. There are special cases where the computetion can be simplifyed, e.g., in a case you mean the Fourier transfer (you are expressed in terms of complex exponents or sin/cos functions), the call function "fourier" (symbolic) or "fft" and "ifft" (numerical) can be used. The new non-uniform Fourier transform functions "nufft" and "nufftn" are announced to be introduced in Matlab 2020a.
3 comentarios
Vladimir Sovkov
el 24 de Dic. de 2019
If you want to learn about the computational functions, just search Matlab Help system for the functions I listed above.
If you want to learn about the mathematics behind your problem (I do not know what your educational background is ...), read any textbook on Functional Analysis; a brief introduction in Wikipedia is, e.g., at https://en.wikipedia.org/wiki/Functional_analysis
Vladimir Sovkov
el 24 de Dic. de 2019
I misprinted in the 1st part of my answer. Must be "integral" but not "inegral".
Más respuestas (0)
Ver también
Categorías
Más información sobre Calculus en Help Center y File Exchange.
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!