It is apparent from the number of interpolation algorithms that people have invented that aliasing is an old problem, and so naturally many previous authors have used terms like ``dealias'' and ``antialias,'' with slightly different connotations. In this thesis, I follow the examples of numerous SEP alumni (and others), and use the term ``antialias'' to refer to methods which remove aliasing without changing sampling rates, by lowpass filtering the data in some manner Claerbout (1992a); Lumley et al. (1994). I use the term ``dealias'' to refer to methods which maintain frequency and change sampling, by inventing some hypothetical data to represent or supplement the original Manin and Spitz (1995); Nichols (1992); Ronen (1990). This seems as good a convention as any, though counter examples can be turned up Beasley and Mobley (1998). Finally, where data are said to be unaliased, I simply mean that in their original state, without any particular sort of manipulation, the data are not aliased.