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The Voigt profile is a model shape of spectral lines, i.e., a model line profile. Its shape described by the Voigt function, which is a convolution combining two distribution functions that model the effects of two types of line broadening: Doppler broadening and pressure broadening. (These, and the result, are termed line broadening functions, or broadening functions, or BFs.) The math offers a means of analyzing a line regarding the two effects, separately and combined.
Voigt-function approximations have been developed because such convolutions are a computational challenge. With today's computing power, the approximations still may be useful for cases where such a model's calculation must be done many times, or for back-of-the-envelope estimates.