| Re: FFT and ROTATE [message #62358 is a reply to message #62357] |
Thu, 04 September 2008 04:55   |
Wox
Messages: 184
Registered: August 2006
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Senior Member |
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On Wed, 3 Sep 2008 15:20:19 -0700 (PDT), wheinz@gmail.com wrote:
> Hello,
>
> I have been wrestling with the FFT and ROTATE functions recently. One
> of the properties of the Fourier transform is that the transform of a
> rotated object is equal to the rotation of the transform of the
> unrotated object. To test this in IDL, I took the FFT of an nxn array
> (called image) and the FFT of that array rotated 90 degrees, image90 =
> ROTATE(image,1). Then, I sorted the real and imaginary parts of the
> coefficients of the results of the FFTs and compared the sorted
> values. I expected that the sorted list of real parts from the FFT of
> the original and rotated arrays would be identical, and that the same
> would be true for the imaginary parts. This is not the case. The sets
> of the magnitudes of the coefficients are equal, as expected.
First of all, care must be taken when rotating the fourier transform.
Check IDL help on this: you have to shift with half the image size in
both directions. I also noticed that it only works with uneven image
sizes (i.e. rotation around the center pixel). Anyway, check the code
below:
pro rotFFTtest
;;load an image
fn = filepath('md1107g8a.jpg',SUBDIRECTORY='examples/data')
image=bytarr(251,251)
image[0,0]= read_image(fn)
image90 = rotate(image,1)
;display the images
window,0
tvscl,image,0
tvscl,image90,1
n = size(image,/dim)
nfreq=n/2+1 ; # positive freq in each dim
nfreq_m=nfreq-1-(~(n mod 2)) ; # negative fequencies in each dim
;;take fft of image, then get the real and imaginary parts
f = fft(image)
f = shift(f,-nfreq[0],-nfreq[1])
f90_1 = rotate(f,1)
f90_1 = shift(f90_1,nfreq[0],nfreq[1])
;;take the fft of image90 then get the real and imaginary parts.
f90_2 = fft(image90)
tvscl,fft(f90_1,/inverse),2
tvscl,fft(f90_2,/inverse),3
end
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