• This property states that the convolution of signals in the time domain will be transformed into the multiplication of their Fourier transforms in the frequency domain.

• Proof :

• The convolution of the two signals in the time domain is defined as,

• Taking the Fourier transform of the convolution.

• Multiply and divide the RHS of the equation (3) by e^(-j2πfλ) to get,

• Let (t-λ) = m in equation (3)

• Using the definition of the Fourier transform of the RHS we get,

  ∴ F[$x_1 (t)* x_2 (t)]=X_1 (f)X_2 (f)$

This is the required result.