It's much easier to get an intuitive understanding of convolution directly in the time domain, without worrying about Fourier Transforms. Convolution with a to

It's much easier to get an intuitive understanding of convolution directly in the time domain, without worrying about Fourier Transforms. Convolution with a top-hat kernel is just a moving average. Each point of the output is the average of the input signal over a given radius about that point. Convolution with other kernels is a weighted moving average. Each point of the output is the average of the input signal over a region with weights depending on the displacement from that point. The Fourier Transform allows implementing convolution as multiplication in frequency space (because the Fourier transform turns translations into multiplications), which is sometimes formally useful, and sometimes more efficient to evaluate.