Here are some questions for you to see if you really know what's happening 
during spectral encoding. I have been told they are quite hard. Answers 
appear below all the questions.


1. In this module, the equations shown were for converting spatial data into
spectral information, but spatial data was always the source. Is it possible to
sample naturally occuring data as spectral data directly?

a) Yes, but it's really difficult.
b) Yes, and it's easy.
c) No, it can't be done.
d) What is spectral data?


2. Transforms have been shown using exponential and cosine functions. Can other
functions be used as spatial/spectral transforms.

a) Yes, easily.
b) Yes, but with difficulty.
c) No.


3. If a spatially encoded source image is converted into spectral data via a DCT,
rotated about its centre and then converted back into spatial data, will the
resulting image simply be the original image rotated about the centre?

a) Yes.
b) No.


4. Can useful transformations be made to data in spectral space?

a) Yes, any transformation can be performed.
b) Yes, but only some transformations.
c) No, except for transforming it back to spatial data.






Answers.

1. Yes, this can be done quite easily. Instead of sampling the amplitude (power)
of a wave at a particular point in time, the power of a frequency band can be
sampled over a period of time. The graphic equaliser display on most modern
stereo systems is a prime example of a waveform being split into many frequency
bands. The spatial/spectral conversion is being performed using filtering
electronics in this case.


2. Yes easily. In fact wavelet transforms involve alternative functions. Probably the
simplest function which can be sensibly used is a step function, or square wave.


3. No. The space (u, v) of the spectral data does not map directly to the spatial
data (x, y). However, if the spectral data was rotated by the top left corner
(the DC component) in increments of 90 degrees with wrapping, the result would be
the same as the source image rotated the same amount. An image which has been
Fourier transformed can be rotated by an arbitrary amount about it centre to
produce a rotated source image.


4. Yes, but it only some transforms are possible (or sensible). It is not 
possible to simply shift a whole image 20 pixels to the right in spectral 
space but bluring an image is an simple operation.