Explain why the aliasing happens in the lighthouse image by

Explain why the aliasing happens in the lighthouse image by using a “frequency domain” explanation. In other words, estimate the frequency of the features that are being aliased. Give this frequency as a number in cycles per pixel. (Note that the fence provides a sort of “spatial chirp” where the spatial frequency increases from left to right.) Can you relate your frequency estimate to the Sampling Theorem? You might try zooming in on a very small region of both the original and downsampled images

Aliased Image:

load lighthouse; %assigns to xx
%downsampling by a factor of p
%xp = xx(1:p:end,1:p:end);
xp = xx(1:2:end,1:2:end);
size(xp)
imshow(xp)

Figure 1 Fiqure 1 File Edit View Iert Tools Desktop Window Help ile 9

Solution

Aliasing is nothing but misidentification of a frequency.Aliasing happens because the light house image is down sampled by a factor of 2,so the sampling rate is lower than the original image .The spatial frequency of the fence increases from left to right in original image.According to the sampling theorem,the sampling rate is less then twice the spatial frequency then it causes Aliasing .Therefore ,the downsampled image the right fence may have the aliasing but we can\'t see the fence clearly.