So this is L2, this is L1.

And here I padded it with 0s.

I take the DFTs, I multiply them in the discrete frequency domain, and

I take the inverse DFT, and I come back to the spatial domain.

And as I mentioned earlier side, slide,

the result then is the circular convolution.

Which is formed by the periodic extension of the linear convolution shown here.

But since the periodic extension is going to be

with respect to l1, l2 would clearly see here.

That there is not going to be another lab between the replicas of this signal yl.

And therefore, the result of the secular

linear convolutions is going to be identical.

[SOUND].

We show here the periodic extension of the result of the

linear convolution with periods L1, L2, as explained in the previous slide.

So in this particular case, there's no aliasing L1, L2 are chosen appropriately.

If instead I choose an L 1 prime which is less than L 1 and

L 2 prime which is less than L2 performing the periodic extension.

And L 1, L 2 prime by the way, are the size of the DFTs.

Then clearly aliasing is going to take place so the resulting image.

Which has size L 2 prime L 1 prime is going to have

the, so many first rows and columns aliased.

And the number of the aliased rows here.

This is L 1 minus L 1 prime.

And the number of the columns that are aliased is L2 minus L2 prime.