## What is the Fourier transform of the convolution?

## 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!):

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