The failure of an asperity, i.e., the dynamic rupture of a small fault area with finite stress drop surrounded by a broken or weak fault area which has no stress drop but which slips after the asperity fails, is proposed as a model for the rupture process of a subevent in a composite earthquake. The rupture area of the composite earthquake surrounding the subevent is modeled by the weak fault area surrounding the asperity in the subevent model. The resulting seismic moment of the subevent is proportional to the stress drop and the rupture area of the subevent, as well as the radius of the composite earthaquake. By setting the stress drops of the asperity models equal to the dynamic stress drops of the subevents, the composite earthquake can be modeled as the sum of a set of subevents which cover the rupture area of the composite earthquake. The scaling of the high- and low-frequency radiation from composite earthquakes composed of asperities is commensurate with generally observed spectral scaling laws, in contrast to composite earthquakes composed of cracks, or smaller earthquakes. A simple filtering strategy is proposed for filtering the waveforms radiated by cracks to approximate the waveforms radiated by asperities. The P and S waves radiated by an ML = 5.2 earthquake which occurred on 9 May 1983, at Coalinga, California, are simulated using the P and S waves radiated by an ML = 3.6 aftershock. The aftershock waveforms are first filtered to approximate the radiation from asperities with the appropriate rupture areas, and then the waveforms of 12 asperity subevents are summed together to simulate the waveforms and spectra of the composite earthquake.