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Digital synthesis of music has led to the consideration of models other than the usual additive (Fourier) synthesis of waveforms. One of these methods, based on the FM equation, has been found to be of particular value due to its easy implementation and the richness and evolutionary character of its harmonic structure in time. Any useful synthesis procedure should be accompanied by a corresponding analytic procedure. In this paper we lay the foundations for such a procedure based on the discrete Hilbert transform.