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blue_leaf77

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I thought the FT was about decomposing images into different frequencies. So I was showing the inverse of what I thought the FT and asking if it was correct as it was easier for me to show it this way.

Is what I showed not related?

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blue_leaf77

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What are R and L?

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Khashishi

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Right and left (referrring to the images)What are R and L?

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Ok, in addition then which of the two examples shown correctly represents the transformation between the spatial domain (right) and domain (left)

I am only learning the FT to gain a very crude understanding of how image reconstruction is done. As I do not have a physics background the course organiers are not teaching the maths

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blue_leaf77

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To me, the bottom picture seems to correspond to a pair of Fourier transform conjugates (can you see why?).Ok, in addition then which of the two examples shown correctly represents the transformation between the spatial domain (right) and domain (left)

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Presumably because it is symmetrical about the centre of k-space.To me, the bottom picture seems to correspond to a pair of Fourier transform conjugates (can you see why?).

But as the image only displays a single frequency I wasn't sure if I only needed to display two conugate pairs or lots

By your answer am I correct in assuming you think the bottom image is correct then?

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blue_leaf77

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A way of justifying the bottom images is to do the math. The right picture of the bottom pair looks like it being composed of three delta functions. Mathematically, it readsPresumably because it is symmetrical about the centre of k-space.

But as the image only displays a single frequency I wasn't sure if I only needed to display two conugate pairs or lots

By your answer am I correct in assuming you think the bottom image is correct then?

$$

f(x,y) = \delta(y) (\delta(x+a) + \delta(x) + \delta(x-a))

$$

Now Fourier transform ##f(x,y)## and see if you will get something that resembles the left picture.

- #12

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Hi. Like I said I don't know any of the maths so I am learning everything conceptually.A way of justifying the bottom images is to do the math. The right picture of the bottom pair looks like it being composed of three delta functions. Mathematically, it reads

$$

f(x,y) = \delta(y) (\delta(x+a) + \delta(x) + \delta(x-a))

$$

Now Fourier transform ##f(x,y)## and see if you will get something that resembles the left picture.

So I don't really know what you mean by 3 delta functions :(

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blue_leaf77

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FT is one subject of math, there is no other way to learn FT except by learning the maths.Like I said I don't know any of the maths so I am learning everything conceptually.

Delta functions is a mathematical object usually used to represent a zero-dimensional point. In reality obviously there is no such object, however if a pinhole is much smaller compared to the wavelength of light illuminating it (in the case of the diffraction of light), it can be modeled as a delta function.

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I see. well thank you for the confirmation but as I have a very limited knowledge of calculus it seems like it'll be a long time before I can prove why the bottom image is correct.FT is one subject of math, there is no other way to learn FT except by learning the maths.

Delta functions is a mathematical object usually used to represent a zero-dimensional point. In reality obviously there is no such object, however if a pinhole is much smaller compared to the wavelength of light illuminating it (in the case of the diffraction of light), it can be modeled as a delta function.

Thanks again for your help though :)

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thanks :)

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