## Convolution Theorem

The convolution theorem for Fourier transforms states that convolution in the time domain equals multiplication in the frequency domain. The continuous-time convolution of two signals and is defined by

 (B.15)

The Fourier transform is then

or,

 (B.16)

Exercise: Show that

 (B.17)

when frequency-domain convolution is defined by

 (B.18)

where is in radians per second, and that

 (B.19)

when frequency-domain convolution is defined by

 (B.20)

with in Hertz.

Next Section:
Flip Theorems
Previous Section:
Modulation Theorem (Shift Theorem Dual)