The NMR spectra for quadrupolar nuclei in solids contain a great deal of structural information. The evaluation of quadrupolar coupling constants, asymmetry parameters, isotropic chemical shifts, chemical shift spans, chemical shift skews and the angles relating the electric field gradient tensor to the chemical shift tensor is typically done by simulating the NMR spectrum with suitable software and fitting the simulated spectrum to the experimental data. Almost always, the spectra of quadrupolar nuclei in solids have been simulated using perturbation theory where the quadrupolar interaction is treated as a perturbation on the much larger Zeeman interaction. With the recent developments in the collection of ultra-wide line NMR spectra, quadrupolar nuclei with larger and larger quadrupolar coupling constants are being studied by NMR and the perturbation approach may not be valid. Errors between simulated and experimental spectra appear when the Larmor frequency is not significantly larger than the quadrupolar coupling constant.