What does convolution theorem mean?
Definitions for convolution theorem
con·vo·lu·tion the·o·rem
This dictionary definitions page includes all the possible meanings, example usage and translations of the word convolution theorem.
Wikipedia
Convolution theorem
In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two signals is the pointwise product of their 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, not standard multiplication. The tensor product symbol ⊗ {\displaystyle \otimes } is sometimes used instead.) 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 F { f ∗ g } = F { f } ⋅ F { g } {\displaystyle {\mathcal {F}}\{f*g\}={\mathcal {F}}\{f\}\cdot {\mathcal {F}}\{g\}} where ⋅ {\displaystyle \cdot } denotes point-wise multiplication.
Numerology
Chaldean Numerology
The numerical value of convolution theorem in Chaldean Numerology is: 5
Pythagorean Numerology
The numerical value of convolution theorem in Pythagorean Numerology is: 1
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"convolution theorem." Definitions.net. STANDS4 LLC, 2024. Web. 27 Apr. 2024. <https://www.definitions.net/definition/convolution+theorem>.
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