Now ... what is Aliasing?
To answer that question, we must enter the frequency domain. In particular, it is important to understand what happens to the frequency spectrum of a function that is sampled.
Put briefly, a sampled function has a frequency spectrum that is the same as the un--sampled function, except that the original spectrum has an infinite number of aliases (other copies of the spectrum of the unsampled function) that are shifted along the frequency axis. One may imagine the original spectrum of a function f as a bump. When we sample f, the resulting frequency spectrum becomes an infinite number of bumps identical to the one associated with f but shifted all over the frequency axis. When the function is reconstructed, this may be a problem if either f was not properly band--limited or if the reconstruction filter is too wide in the frequency domain. In either case, we introduce frequency components that do not belong to the original function.
In this seminar, some of the basics of signal analysis are reviewed in a brief and intuitive way: The fourier transform, convolution, the delta function, sampling & c. After these preliminaries, an attempt is made to uncover the true nature of aliasing.
Finally, some examples of aliasing artifacts and their remedies are presented. The examples are mainly in 2D, but aliasing is even more of a problem in volume graphics since, here, the signal analysis issues turn up, not only in the rendering phase, but also in the discrete 3D representation of the geometric objects.