The Fourier-related transforms that operate on a function over a finite domain, such as the DFT or DST or a Fourier series, can be thought of as implicitly defining an "extension" of that function outside the domain. That is, once you write a function formula_1 as a sum of sinusoids, you can evaluate that sum at any formula_2, even for formula_2 where the original formula_1 was not specified. The DFT, like the Fourier series, implies a periodic extension of the original function. A DST, like a sine transform, implies an odd extension of the original function.