Finite Fourier Transform on a 3d wave

  • Thread starter brandy
  • Start date
  • #1
161
0
Finite Fourier Transform on a 2d wave

How does the finite fourier transform work exactly?

The transform of f(x) is
[itex]\widetilde{f}(\lambda_{n})[/itex] =[itex]\int[/itex][itex]^{L}_{0}[/itex] f(x) X[itex]_{n}[/itex] dx

If I had a 3d wave equation pde and I applied Finite fourier transform on the pde for
z(x,y,t)=X(x)Y(y)T(t)

f(x)=z[itex]_{xx}[/itex]
[itex]\tilde{z_{xx}(\lambda_{n})}[/itex] =[itex]\int[/itex][itex]^{L}_{0}[/itex] z[itex]_{xx}[/itex] X[itex]_{n}[/itex](x) dx

f(x)=z[itex]_{yy}[/itex]
[itex]\tilde{z_{yy}(\lambda_{n})}[/itex] =[itex]\int[/itex][itex]^{L}_{0}[/itex] z[itex]_{yy}[/itex] Y[itex]_{n}[/itex](y) dy

etc for T

or

is the transform the same for everything, namely:
f(x)=z[itex]_{xx}[/itex]
[itex]\tilde{z_{xx}(\lambda_{n})}[/itex] =[itex]\int[/itex][itex]^{L}_{0}[/itex] z[itex]_{xx}[/itex] X[itex]_{n}[/itex](x) Y[itex]_{n}[/itex](y) dx

or is it a double integral?
or do you apply finite fourier twice with respect to y and x.
 
Last edited:

Answers and Replies

  • #2
I like Serena
Homework Helper
6,577
176
Hi brandy! :smile:

You can take any transform you want, including a 3D fourier transform, which would be a triple integral.
And also a transform of for instance ##z_{xx}## with respect to y.

In all cases you can apply the Fourier's theorems.
It's just a matter of what you want to achieve.
 
  • #3
jasonRF
Science Advisor
Gold Member
1,346
402
Note that you should have a different "frequency" variable for each dimension $x$ and $y$.
 

Related Threads on Finite Fourier Transform on a 3d wave

Replies
3
Views
5K
Replies
2
Views
981
Replies
4
Views
2K
Replies
0
Views
4K
  • Last Post
Replies
8
Views
665
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
3
Views
2K
Replies
3
Views
5K
Replies
3
Views
2K
  • Last Post
Replies
3
Views
1K
Top