Fast Analysis/Synthesis of Harmonic Signals

Harmonic models are commonly used in signal processing. The analysis of harmonic signals requires the solution of a symmetric Toeplitz system of equations. Levinson-based Toeplitz solvers have a O(n ²) complexity. This paper proposes an O(n) algorithm by encoding the inverse matrices required for the solution of the linear system to a few parameters in order to obtain an approximate solution for the harmonic model. For speech related applications, the proposed algorithm is 2-30 times faster than the Levinson algorithm, while degradation is minimal and memory requirements are very low