# Blog

## What is the convolution theorem in physics?

• In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise 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 ).

## What is the convolution of two functions?

• The FFT & Convolution The convolution of two functions is deﬁned for the continuous case The convolution theorem says that the Fourier transform of the convolution of two functions is equal to the product of their individual Fourier transforms We want to deal with the discrete case

## What is the linearity of Fourier transform?

• Linearity Linear combination of two signals x1(t) andx2(t) is a signal of the formax1(t) +bx2(t). Linearity Theorem: The Fourier transform is linear; that is, given twosignals x1(t) andx2(t) and two complex numbers aandb, then ax1(t) +bx2(t),aX1(j!) +bX2(j!):