Assignment
Due Tuesday, November
Students may work individually or in pairs on this assignment.
Modify the ‘base’ program provided in this archive to add the
following features:
0. Run the code. Press ‘?’ to see the options. Read and understand
all of the code,
including the Complex class, which you will use.
1. Implement the FFT() function. The necessary bit-reversal code is
provided.
You should use the main FFT code from class.
[2 marks] FFT code from class
2. Implement the FFT2D() function. See the comments in that function.
[2 marks] rows computation
[2 marks] column computation
3. Implement the forwardFFT2D() function. This just sets up the data
and calls FFT2D(). But the data must be slightly modified so that
the F.T. is centred in the window at (N/2,N/2).
[2 marks] copy and centre (a bit tricky to get (-1)^(x+y) correct)
[1 mark] call FFT2D() appropriately
4. Implement the inverseFFT2D() function. This uses the FFT2D() as a
black box, so requires that the conjugate of the F.T. be input to
the black box, and that the real component of the result be stored
after the computation is done. You must normalize the real
component (think about this). You must also undo the effect of
centring in step 3, above.
[1 mark] form a copy of the complex conjugate
[1 mark] call FFT2D() appropriately
[1 mark] extract real part and normalize
[1 mark] undo centring
5. Once the code works, use it to explore the FFT of the circle and
gaussian images. Do not hand anything in for this. [0 marks]
6. Use your code to remove the noise from the noisy1.jpg, noisy2.png,
and noisy3.png. Submit the de-noised images and the F.T. of the
de-noised images.
[1 mark] good denoising of noisy1.jpg and noisy2.png
[1 mark] good denoising of noisy3.jpg
7. Email archive containing these eight
files, with exactly these names:
[1 mark] for following these submission instructions *exactly*
base.pde your code
readme.txt your names and student numbers and any
comments you want to provide
noisy1-denoised.png de-noised noisy1.jpg
noisy1-ft.png 2D Fourier transform of de-noised noisy1.jpg
noisy2-denoised.png de-noised noisy2.png
noisy2-ft.png 2D Fourier transform of de-noised noisy2.png
noisy3-denoised.png de-noised noisy3.png
noisy3-ft.png 2D Fourier transform of de-noised noisy3.png