Optimal parameters of a sinusoidal representation of signals

A. Kocsor,   L. Toth,   I. Balint

In the spectral analysis of digital signals, one of the most useful parametric models is the representation by a sum of phase-shifted sinusoids in form of , where and are the component’s amplitude, frequency and phase, respectively. This model generally fits well speech and most musical signals due to the shape of the representation functions. If using all of the above parameters, a quite di±cult optimization problem arises. The applied methods are generally based on eigenvalue decomposition [3]. However this procedure is computationally expensive and works only if the sinusoids and the residual signal are statistically uncorrelated. To speed up the representation process also rather ad hoc methods occur [4]. The presented algorithm applies the newly established Homogeneous Sinus Representation Function (HSRF) to find the best representing subspace of fixed dimension N by a BFGS optimization. The optimum parameters ensure the mean square error of approximation to be below a preset threshold.