In this project, Spectral Envelopes in Sound Analysis and Synthesis, various methods for estimation, representation, file storage, manipulation, and application of spectral envelopes to sound synthesis were evaluated, improved, and implemented. A prototyping and testing environment was developed, and a function library to handle spectral envelopes was designed and implemented. For the estimation of spectral envelopes, after defining the requirements, the methods LPC, cepstrum, and discrete cepstrum were examined, and also improvements of the discrete cepstrum method (regularization, stochastic (or probabilistic) smoothing, logarithmic frequency scaling, and adding control points). An evaluation with a large corpus of sound data showed the feasibility of discrete cepstrum spectral envelope estimation. After defining the requirements for the representation of spectral envelopes, filter coefficients, spectral representation, break-point functions, splines, formant representation, and high resolution matching pursuit were examined. A combined spectral representation with indication of the regions of formants (called fuzzy formants) was defined to allow for integration of spectral envelopes with precise formant descriptions. For file storage, new data types were defined for the Sound Description Interchange Format (SDIF) standard. Methods for manipulation were examined, especially interpolation between spectral envelopes, and between spectral envelopes and formants, and other manipulations, based on primitive operations on spectral envelopes. For sound synthesis, application of spectral envelopes to additive synthesis, and time-domain or frequency-domain filtering have been examined. For prototyping and testing of the algorithms, a spectral envelope viewing program was developed. Finally, the spectral envelope library, offering complete functionality of spectral envelope handling, was developed according to the principles of software engineering.