Relationship Between Convolution and Fourier Analysis

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While I am reading a lecture note about a rendering of lighting and its reflection on surfaces, I've found the following change of formula using Fourier Analysis



enter image description here



The author appended the following slides too, but can't understand how to formula converted with those hints.



Any hint for good starting of understanding this conversion?



The full lecture note is available at link



enter image description here




fourier-analysis convolution




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  • The Fourier transform of a convolution is a product and vice versa: $$widehatf*g = hat f cdot hat g$$ (with some factor depending of what definition of Fourier transform is being used.)
    – md2perpe
    Jul 15 at 7:26










  • Only for circular convolution which the above is not.
    – mathreadler
    Jul 15 at 7:40










  • @md2perpe product of what?
    – Beverlie
    Jul 15 at 8:06










  • @Beverlie. The Fourier transform of convolution of two functions is the product of the Fourier transforms of the two functions.
    – md2perpe
    Jul 15 at 8:25










  • @mathreadler. What kind of convolution is this? I don't want to deep-dive into the formulas right now.
    – md2perpe
    Jul 15 at 8:27














up vote
1
down vote

favorite












While I am reading a lecture note about a rendering of lighting and its reflection on surfaces, I've found the following change of formula using Fourier Analysis



enter image description here



The author appended the following slides too, but can't understand how to formula converted with those hints.



Any hint for good starting of understanding this conversion?



The full lecture note is available at link



enter image description here




fourier-analysis convolution




share|cite|improve this question





















  • The Fourier transform of a convolution is a product and vice versa: $$widehatf*g = hat f cdot hat g$$ (with some factor depending of what definition of Fourier transform is being used.)
    – md2perpe
    Jul 15 at 7:26










  • Only for circular convolution which the above is not.
    – mathreadler
    Jul 15 at 7:40










  • @md2perpe product of what?
    – Beverlie
    Jul 15 at 8:06










  • @Beverlie. The Fourier transform of convolution of two functions is the product of the Fourier transforms of the two functions.
    – md2perpe
    Jul 15 at 8:25










  • @mathreadler. What kind of convolution is this? I don't want to deep-dive into the formulas right now.
    – md2perpe
    Jul 15 at 8:27












up vote
1
down vote

favorite









up vote
1
down vote

favorite











While I am reading a lecture note about a rendering of lighting and its reflection on surfaces, I've found the following change of formula using Fourier Analysis



enter image description here



The author appended the following slides too, but can't understand how to formula converted with those hints.



Any hint for good starting of understanding this conversion?



The full lecture note is available at link



enter image description here




fourier-analysis convolution




share|cite|improve this question













While I am reading a lecture note about a rendering of lighting and its reflection on surfaces, I've found the following change of formula using Fourier Analysis



enter image description here



The author appended the following slides too, but can't understand how to formula converted with those hints.



Any hint for good starting of understanding this conversion?



The full lecture note is available at link



enter image description here





fourier-analysis convolution





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 15 at 5:20
























asked Jul 15 at 4:31









Beverlie

1,078318




1,078318











  • The Fourier transform of a convolution is a product and vice versa: $$widehatf*g = hat f cdot hat g$$ (with some factor depending of what definition of Fourier transform is being used.)
    – md2perpe
    Jul 15 at 7:26










  • Only for circular convolution which the above is not.
    – mathreadler
    Jul 15 at 7:40










  • @md2perpe product of what?
    – Beverlie
    Jul 15 at 8:06










  • @Beverlie. The Fourier transform of convolution of two functions is the product of the Fourier transforms of the two functions.
    – md2perpe
    Jul 15 at 8:25










  • @mathreadler. What kind of convolution is this? I don't want to deep-dive into the formulas right now.
    – md2perpe
    Jul 15 at 8:27
















  • The Fourier transform of a convolution is a product and vice versa: $$widehatf*g = hat f cdot hat g$$ (with some factor depending of what definition of Fourier transform is being used.)
    – md2perpe
    Jul 15 at 7:26










  • Only for circular convolution which the above is not.
    – mathreadler
    Jul 15 at 7:40










  • @md2perpe product of what?
    – Beverlie
    Jul 15 at 8:06










  • @Beverlie. The Fourier transform of convolution of two functions is the product of the Fourier transforms of the two functions.
    – md2perpe
    Jul 15 at 8:25










  • @mathreadler. What kind of convolution is this? I don't want to deep-dive into the formulas right now.
    – md2perpe
    Jul 15 at 8:27















The Fourier transform of a convolution is a product and vice versa: $$widehatf*g = hat f cdot hat g$$ (with some factor depending of what definition of Fourier transform is being used.)
– md2perpe
Jul 15 at 7:26




The Fourier transform of a convolution is a product and vice versa: $$widehatf*g = hat f cdot hat g$$ (with some factor depending of what definition of Fourier transform is being used.)
– md2perpe
Jul 15 at 7:26












Only for circular convolution which the above is not.
– mathreadler
Jul 15 at 7:40




Only for circular convolution which the above is not.
– mathreadler
Jul 15 at 7:40












@md2perpe product of what?
– Beverlie
Jul 15 at 8:06




@md2perpe product of what?
– Beverlie
Jul 15 at 8:06












@Beverlie. The Fourier transform of convolution of two functions is the product of the Fourier transforms of the two functions.
– md2perpe
Jul 15 at 8:25




@Beverlie. The Fourier transform of convolution of two functions is the product of the Fourier transforms of the two functions.
– md2perpe
Jul 15 at 8:25












@mathreadler. What kind of convolution is this? I don't want to deep-dive into the formulas right now.
– md2perpe
Jul 15 at 8:27




@mathreadler. What kind of convolution is this? I don't want to deep-dive into the formulas right now.
– md2perpe
Jul 15 at 8:27















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