Direct Digital Synthesis (DDS)
DDS is described in two IEEE Signal Processing Magazine (see  and ) and in a chapter of a book .
Years ago, I built this hardware DDS with TTL logic and a low-cost DAC, based upon the EDN  article. It still works like a charm! Since then, I have been using hardware and software DDS for various purpose:
High resolution, digital software clocks (from the days of the IBM AT until the last past years, for embedded systems).
Software timebase for slow scan television (SSTV, see  and F2DC homepage).
Various attempts at software synthesizers (the so-called electronics organs).