Granular synthesis has been used for a number of years as a sound synthesis technique. This method constructs an acoustic signal from a number of short-duration acoustic elements, called grains. These grains are produced either by extracting short segments of natural sounds such as speech, or by synthesis according to a mathematical description of the grains. Efficient methods of producing and combining these grains are currently especially interesting, because the recent development of special-purpose digital signal processing (DSP) microprocessors has made real-time granular synthesis possible at a reasonable hardware cost. This paper discusses the computational aspects of granular synthesis. Methods of extracting grains from natural signals and recombining them with phase alignment are described. Fast methods for digital generation of synthetic signals with linear frequency modulation (FM) are also presented.