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From: glen herrmannsfeldt on 3 Aug 2010 18:09
Dirk Bell <bellda2005(a)cox.net> wrote:
> On Jul 30, 5:34�pm, glen herrmannsfeldt <g...(a)ugcs.caltech.edu> wrote:
>> niyander <mightycatniyan...(a)gmail.com> wrote:
>> > can anyone tell me how to perform 2d fft? what i understood for 2d fft
>> > is that for each rows we perform individual fft's and place the result
>> > on the respective rows and similarly for the columns. what i mean is
>> > suppose i have an array of 2d data as:
>> > 0000
>> > 0110
>> > 0110
>> > 0000

>> The FFT is separable in rectangular coordinates. �You separately
>> do the X and Y transforms, in either order, to get the appropriate
>> XY (2D) transform.

(snip)

> Actually, what he is saying will not give the same result as a 2-D
> fft. After he fft's the rows, the first column is no longer (0000).

Oh, that is what he meant? No, you can't do that.

First you transform each row, leaving the result in that row.
Then, with the row results in each row, you transform each column.
(Or columns and then rows.)

Each element will then have an X and Y frequency, with one
corner being the (0,0) or DC term. These correspond to the
possible vibrational modes of a square drum head. The (0,0)
mode is the one where the whole drum surface moves up and down
together, and has the lowest frequency. The (0,1) and (1,0)
modes are degenerate, that is, both have the same frequency,
such that any linear combination of them will also have that
frequency.

For a rectangular drum head with non-commensurate side lengths
there will be 16 different modes, all with different frequencies.
The (i,j) gives the number if X and Y nodes, respectively.

Well, you should actually use the sine transform for drum heads,
but the modes will be somewhat similar.

-- glen
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