Refer to the online manuals for use of buttons (such as `fft` and `rmdc`)
in the `Imcalc Tool`.
Construct the FFT of an image selected from `images` directory and see if you can relate it's
main features back to the original image. Notice that the result is in the form of a complex image,
as it must be for a Fourier transform. This is shown by the `Image type` cast bar, which
is set to the image type on completion of a calculation, and can also be used to re-cast the
data (so that a complex image can be converted to and from two floating point images).

You will encounter the first problem
associated with image processing, although the software has automatic data windowing,
the dynamic range of computed quantities prevents
simple visulalisation of unmodified result. You may have to remove the DC component using
the `rmdc` button or select a region of interest in order to see any structure, there are
also many non-linear processes which can be performed which will also help.

Try barrel shifting the FFT and the applying the inverse FFT, what do you see and why?

Use the `Create Tool` to generate Gaussian random noise on each pixel and the add
this to the original image (the `noise` button generates and image of grey levels
with a zero mean Gaussian distribution and the `noise` variable controls the
variance).

Design a systematic set of tests to investigate the behaviour of the real
and imaginary components of the FFT of the image for various additive noise levels.
Use the image histogram and the `noise` button to estimate the variance of the
image for different levels of noise.

Attempt to find answers to the following questions:

- Do you see any correlation between the level of added noise and the noise in the
Fourier domain? Try investigating this by plotting a graph of FFT noise against original
image noise for various values of additive noise.
- Do your results depend on the data in the original image? (You can use the
`Create Tool`to generate a few alternatives such as the checkerboard). - Given that you know how much noise there is in the noisy FFT image can you find a
way of estimating this without subtracting the original image?
- If you were to apply a filter to a Fourier domain image (as described by the
convolution theorem) what would be the consequences in terms of the noise on the
inverse? (Start by thinking about one sinusoidal component).