Numericaly Inverse Fourier Transform

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Dear community of Mathematics,



Suppose that I have a PDE to solve:



I transform the equation from time (t) domain into the frequency domain (omega) via Fourier transform and then I solve it.



In order to return back into the time domain I have three options :



a) analytical inverse fourier,
b) numerical integration and c) evaluate the function on a grid (regular in each dimension) and apply inverse FFT.



I want to ask about the third option (c):
I want to make a grid by evaluating the function at different values of omega (which is in the frequency domain) how can I do this. At what omegas I will evaluate the function, complex or real ones?. At what range?



I have not experience on this at all. I would appreciate if anyone can guide me on this by giving me some insights on the steps i need to follow.



Thank you in advance.










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  • Are you asking about trigonometric interpolation?
    – Mattos
    Sep 10 at 2:55










  • I am not sure that it is trigonometric interpolation
    – Edmond Muho
    Sep 15 at 12:06














up vote
1
down vote

favorite
1












Dear community of Mathematics,



Suppose that I have a PDE to solve:



I transform the equation from time (t) domain into the frequency domain (omega) via Fourier transform and then I solve it.



In order to return back into the time domain I have three options :



a) analytical inverse fourier,
b) numerical integration and c) evaluate the function on a grid (regular in each dimension) and apply inverse FFT.



I want to ask about the third option (c):
I want to make a grid by evaluating the function at different values of omega (which is in the frequency domain) how can I do this. At what omegas I will evaluate the function, complex or real ones?. At what range?



I have not experience on this at all. I would appreciate if anyone can guide me on this by giving me some insights on the steps i need to follow.



Thank you in advance.










share|cite|improve this question





















  • Are you asking about trigonometric interpolation?
    – Mattos
    Sep 10 at 2:55










  • I am not sure that it is trigonometric interpolation
    – Edmond Muho
    Sep 15 at 12:06












up vote
1
down vote

favorite
1









up vote
1
down vote

favorite
1






1





Dear community of Mathematics,



Suppose that I have a PDE to solve:



I transform the equation from time (t) domain into the frequency domain (omega) via Fourier transform and then I solve it.



In order to return back into the time domain I have three options :



a) analytical inverse fourier,
b) numerical integration and c) evaluate the function on a grid (regular in each dimension) and apply inverse FFT.



I want to ask about the third option (c):
I want to make a grid by evaluating the function at different values of omega (which is in the frequency domain) how can I do this. At what omegas I will evaluate the function, complex or real ones?. At what range?



I have not experience on this at all. I would appreciate if anyone can guide me on this by giving me some insights on the steps i need to follow.



Thank you in advance.










share|cite|improve this question













Dear community of Mathematics,



Suppose that I have a PDE to solve:



I transform the equation from time (t) domain into the frequency domain (omega) via Fourier transform and then I solve it.



In order to return back into the time domain I have three options :



a) analytical inverse fourier,
b) numerical integration and c) evaluate the function on a grid (regular in each dimension) and apply inverse FFT.



I want to ask about the third option (c):
I want to make a grid by evaluating the function at different values of omega (which is in the frequency domain) how can I do this. At what omegas I will evaluate the function, complex or real ones?. At what range?



I have not experience on this at all. I would appreciate if anyone can guide me on this by giving me some insights on the steps i need to follow.



Thank you in advance.







pde fourier-analysis fourier-transform






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asked Sep 9 at 13:50









Edmond Muho

62




62











  • Are you asking about trigonometric interpolation?
    – Mattos
    Sep 10 at 2:55










  • I am not sure that it is trigonometric interpolation
    – Edmond Muho
    Sep 15 at 12:06
















  • Are you asking about trigonometric interpolation?
    – Mattos
    Sep 10 at 2:55










  • I am not sure that it is trigonometric interpolation
    – Edmond Muho
    Sep 15 at 12:06















Are you asking about trigonometric interpolation?
– Mattos
Sep 10 at 2:55




Are you asking about trigonometric interpolation?
– Mattos
Sep 10 at 2:55












I am not sure that it is trigonometric interpolation
– Edmond Muho
Sep 15 at 12:06




I am not sure that it is trigonometric interpolation
– Edmond Muho
Sep 15 at 12:06















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