Polynomial quasi-harmonic models for speech analysis and synthesis

Harmonic plus noise models have been successfully applied to a broad range of speech processing applications, including, among others, low bit-rate speech coding, and speech restoration and transformation. In conventional methods, the frequencies, the relative phases and the amplitudes of the pitch-harmonic components are assumed to be piecewise constants over an analysis frame. This assumption is inadequate in segments where fast variations of these parameters may occur, e.g. phoneme-to-phoneme boundaries or speech onsets. In this contribution, a time-varying model of the pitch-harmonic parameter is presented. It is based on a basis expansion technique, consisting in representing the time-varying functions as a linear combination of fixed basis function. An estimation procedure for the parameters of this expansion is presented. Results are provided to demonstrate the effectiveness of this approach. 1. HARMONIC-PLUS-NOISE MODELS Sinusoidal as well as Harmonic-plus-noise models have been applied with success to solve many speech processing problems. Harmonic-plus-noise model (HNM) assumes the speech signal to be composed of a quasi-harmonic part s(t) and a noise part n(t): x(t) = s(t) + n(t) (1) The quasi-harmonic part, in voiced segments, reflects the (local) periodicity of the speech signal. The noise part n(t) accounts for the cycle-to-cycle variations of the glottal airflow, the friction noise, etc... Harmonic plus noise models have proven to be useful in many speech processing applications, including among others low-bit rate speech coding [6], speech transformation (time scaling, pitch scaling) [3], text-to-speech synthesis and co-channel speaker separation [7]. In a quasi-harmonic model, s(t) is represented as a superposition of almost harmonically related sinusoidal components