Abstract
Statement of Problem
Digital FM synthesis is now widely known as an efficient way of synthesizing musical tones. The basic synthesis method was developed by J.M. Chowning [1] at Stanford University in 1973 and the Yamaha Music Corporation has since created a vast array of musical products based on this technique. The nonlinear FM synthesis equation makes the analysis of this class of signals extremely complex. Recently published methods have uncovered a possible approach to this analysis using discrete phase unwrapping. A method is sought for extracting the FM synthesis parameters from well controlled FM synthesis samples.
Sources of Data
Several different audio samples were created by a software program model which approximates the Yamaha DX7 Digital FM Synthesizer. Two other audio samples of a DX7 oboe and flute were actually digitized using a Casio FZ-1 16-bit sampling synthesizer. The digitized data was then transferred to an Apple MAC SE disk and then to an IBM-PC format disk where the data was analyzed by the algorithm developed in this thesis.
Conclusions Reached
The results of this study qualitatively show that discrete phase unwrapping can be applied to a variety of FM generated signals to extract frequency modulator signals from their carriers. We had hoped for a more robust analysis algorithm that would produce more quantitative results for direct application to the Yamaha DX7. However, with further development we believe that the qualitative results can be used to characterize actual acoustic instrument parameters for application to FM digital music synthesis.