A phase interpolation algorithm for sinusoidal model based music synthesis

This paper presents a least square quadratic phase interpolation algorithm for sinusoidal model based music synthesis. This algorithm uses two additions with one parameter per data frame to generate the phase samples of a component sinewave. Compared with the cubic phase interpolation algorithm proposed by McAulay and Quatieri (1986), the proposed algorithm is more efficient in terms of computational complexity and parameter storage. In the meantime, it also produces smoother frequency tracks (that is, with less spurious oscillations). Unlike the existing quadratic phase interpolation algorithm, where the phase measurements are ignored ("magnitude-only"), the proposed algorithm interpolates phase in a least square sense from both the phase and the frequency measurements at data frame boundaries. Thus the resulting phase samples are approximately "locked" to the measured ones. Informal listening tests on various musical instrument tones indicate that the proposed algorithm clearly outperforms the magnitude-only synthesis approach and is qualitatively comparable to the cubic one.