Today, a DSP would never be put in a general purpose computer as they are limited in what they can do and difficult to program.
That depends on what you mean by general purpose. A lot of home users use their computers for multimedia or games, and some have sound cards in their computers for this purpose, and these will usually contain a DSP. For example, if you had a Sound blaster from the late 90's or later you had a DSP in your computer, and some modern graphics cards have them. The Playstation 4 has one, although it's a quite a stretch to call that a general purpose computer.
Of course, the very name "DSP" implies a non-general purpose, but practically speaking, sound and graphics processing should be covered.
