The convolution-multiplication property is one of the most insightful and useful properties of the Fourier transform and discrete-time Fourier transform. This lesson introduces the convolution-multiplication property for the DFT. Multiplication of DFT coefficients corresponds to circular convolution of time signals. You will gain an understanding of the difference between linear and circular convolution that is critical for properly using the DFT to filter signals.
Circular convolution and using the DFT for filtering are explored in much greater detail in the subsequent two lessons.