Cross modulation or Exponential FM is a sound synthesis technique associated with modular analog subtractive synthesizers. It differs from the more well-known linear FM synthesis technique in that the modulation is an exponential function of the control voltage. Its spectrum shape is more complex, thus giving it a larger bandwidth with respect to the modulation depth. Thus, the prevention of aliasing distortion requires different conditions than Carson’s rule as used with linear FM. A suitable equation will be presented in this paper.

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This paper introduces the Vector Phaseshaping (VPS) synthesis technique, which extends the classic Phase Distortion method by providing flexible means to distort the phase of a sinusoidal oscillator. This is achieved by describing the phase distortion function using one or more breakpoint vectors, which are then manipulated in two dimensions to produce waveshape modulation at control and audio rates. The synthesis parameters and their effects are explained, and the spectral description of the method is derived. Certain synthesis parameter combinations result in audible aliasing, which can be reduced with a novel aliasing suppression algorithm described in the paper. The extension is capable of producing a variety of interesting harmonic and inharmonic spectra, including for instance, formant peaks, while the two-dimensional form of the control parameters is expressive and is well suited for interactive applications.

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