Finite Fourier Transform on a 3d wave

  • Thread starter brandy
  • Start date
  • #1
brandy
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
MHB
16,350
253
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
1,503
567
Note that you should have a different "frequency" variable for each dimension $x$ and $y$.
 

Suggested for: Finite Fourier Transform on a 3d wave

  • Last Post
Replies
4
Views
245
Replies
7
Views
418
Replies
1
Views
1K
Replies
0
Views
79
  • Last Post
Replies
4
Views
2K
Replies
7
Views
1K
  • Last Post
Replies
3
Views
3K
Replies
11
Views
757
Replies
2
Views
67
  • Last Post
Replies
6
Views
936
Top