From lecture: "Convolving an image in the spacial domain is the same thing as multiplying by that filter in the frequency domain". I'm having a hard time understanding exactly how multiplication works in this application - how do you multiply by a filter?

Imagine the Fourier transform of the image and the filter are two 2-dimensional matrices. The multiplication works by multiplying these two matrices in an element-wise manner.

Is there an effective difference in the output image between over sampling and convolution? Is it sometimes better to over sample then to convolve the image and then sample normally?