Optimal parameters of a sinusoidal representation of signals

 A. Kocsor1  L. Tóth1  I. Bálint2  3  4

  Acta Cybernetica 14 (1999) 315-330.

Abstract:

 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 An , , 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 difficult 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.  

Footnotes

  1  MTA-JATE Research Group on Artificial Intelligence, H-6720 Szeged, Aradi Vértanuk Tere 1, Hungary 2  Department of Theoretical Physics, József Attila University, H-6720 Szeged, Tisza L. krt. 80-82., Hungary 3  Department of Pharmaceutical Analysis, Szent-Györgyi Albert Medical University, H-6720 Szeged, Somogyi Béla u. 4., Hungary 4  Department of Natural Scienses, Polytechnic of the Miskolc University, H-2400 Dunaújváros, Táncsics M. u. 1., Hungary