Optimal parameters of a sinusoidal representation of signals
András Kocsor, László Tóth, Imre Bálint · 1999
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 P N 1 n=0 An sin(!n t + 'n ), where An , !n , and 'n are the component's amplitude, frequency and phase, respectively. This model generally ts well speech and most musical signals due to the shape of the representation functions. If using all of the above parameters, a quite dicult 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 nd the best representing subspace of xed dimension N by a BFGS optimization. The optimum parameters fA; !; 'g ensure the mean squar...