Spectral envelopes are very useful in sound analysis and synthesis because of their connection with production and perception models, and their ability to capture and to manipulate important properties of sound using easily understandable ``musical'' parameters.

It is not easy, however, to estimate and represent them well, as several requirements must be fulfilled. We discuss the strengths and weaknesses of the estimation methods LPC, cepstrum, and discrete cepstrum, and evaluate the representations filter coefficients, sampled, break-point functions, splines, and formants. The proposed high-level approach to spectral envelope handling is followed in software developed at IRCAM, which makes some important applications of spectral envelopes in the domain of additive analysis-synthesis possible.