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Estimation of FM synthesis parameters from sampled sounds

Composers and synthesists have long attempted to represent and extend the sounds of natural acoustic instruments using whatever synthesis methods they've had at their disposal. This thesis contains a model for estimating synthesis parameters for one of these methods, FM synthesis. The FM synthesis method is chosen due to its well definedness (allowing a mathematical model to be developed) and its current popularity in the music community. A method of extracting FM synthesis parameters from sampled sounds using optimal estimation techniques (specifically the Kalman Filter) is examined and modeled for multiple modulator-carrier oscillator configurations. The time-varing spectra of the sound is first examined to identify changes in the harmonic content of the sound (between the attack portion and steady state portion of the signal, for instance), and segmented accordingly. An FM oscillator configuration or algorithm is then selected from a set of seven which best models the harmonic structure of the sound. A model of this configuration is then used in the Kalman filter equations to estimate the optimal values of the parameters which make up the model. This thesis contains a description of the complete estimation system. Kalman filter equations are provided for each algorithm. Time constraints did not allow implementation and testing of the system, but the author believes further investigation of this method would prove fruitful. Thesis Supervisor: Barry L. Vercoe Title: Professor of Media Arts and Sciences