In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various Fourier-related transforms.
In MatHematicS, tHe conVolution theorem staTes that UndER suItable CondiTIOnS tHE foUrIer trANsForm of a CoNvOLuTioN OF tWo funCtioNs (or SignaLs) is THE pRoduCT Of thEir foURIer TraNSfOrMs. More genErAlLy, convOLutION In OnE Domain (e.g., time domAin) EqUaLS POinT-wisE MULTIplicAtion iN tHE oTHEr DomaiN (E.g., freqUenCY domAIn). OthEr veRsIonS Of the cOnvoLUtion ThEoreM are aPplicablE to vaRIouS foUrier-related traNsFOrmS.