Kramers–Kronig analysis for parallel electron energy loss spectroscopy (PEELS) data is developed as a software package. When used with a JEOL 4000EX high-resolution transmission electron microscope (HRTEM) operating at 100 keV this allows us to obtain the dielectric function of relatively wide band gap materials with an energy resolution of approx. 1.4 eV. The imaginary part of the dielectric function allows the magnitude of the band gap to be determined as well as the joint-density-of-states function. Routines for obtaining three variations of the joint-density of states function, which may be used to predict the optical and dielectric response for angle-resolved or angle-integration scattering geometries are also described. Applications are presented for diamond, aluminum nitride (AlN), quartz ( SiO 2) and sapphire ( Al 2 O 3). The results are compared with values of the band gap and density of states results for these materials obtained with other techniques.