<Table> <Tr> <Td> </Td> <Td> This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations . Please help to improve this article by introducing more precise citations . (October 2013) (Learn how and when to remove this template message) </Td> </Tr> </Table> <Tr> <Td> </Td> <Td> This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations . Please help to improve this article by introducing more precise citations . (October 2013) (Learn how and when to remove this template message) </Td> </Tr> <P> In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution is the pointwise product of Fourier transforms . In other words, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Versions of the convolution theorem are true for various Fourier - related transforms . Let f (\ displaystyle f) and g (\ displaystyle g) be two functions with convolution f ∗ g (\ displaystyle f * g). (Note that the asterisk denotes convolution in this context, and not multiplication . The tensor product symbol ⊗ (\ displaystyle \ otimes) is sometimes used instead .) </P> <P> If F (\ displaystyle (\ mathcal (F))) denotes the Fourier transform operator, then F (f) (\ displaystyle (\ mathcal (F)) \ (f \)) and F (g) (\ displaystyle (\ mathcal (F)) \ (g \)) are the Fourier transforms of f (\ displaystyle f) and g (\ displaystyle g), respectively . Then </P>

State convolution property in relation to fourier transform
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