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Linear prediction is presented as a spectral modeling technique in which the signal spectrum is modeled by an all-pole spectrum. The method allows for arbitrary spectral shaping in the frequency domain, and for modeling of continuous as well as discrete spectra (such as filter bank spectra). In addition, using the method of selective linear prediction, all-pole modeling is applied to selected portions of the spectrum, with applications to speech recognition and speech compression. Linear prediction is compared with traditional analysis-by-synthesis techniques for spectral modeling. It is found that linear prediction offers computational advantages over analysis-by- synthesis, as well as better modeling properties if the variations of the signal spectrum from the desired spectral model are large. For relatively smooth spectra and for filter bank spectra, analysis-by-synthesis is judged to give better results. Finally, a suboptimal solution to the problem of all-zero modeling using linear prediction is given.