Formant Synthesis of Haegeum: A Sound Analysis/Synthesis System Using Cepstral Envelope

Abstract

This paper presents a formant synthesis method of haegeum using cepstral envelope for spectral modeling. Spectral modeling synthesis (SMS) is a technique that models time-varying spectra as a combination of sinusoids (the "deterministic" part), and a time-varying filtered noise component (the "stochastic" part). SMS is appropriate for synthesizing sounds of string and wind instruments whose harmonics are evenly distributed over whole frequency band. Formants (or acoustic resonances) are extracted from cepstral envelope and we use them for synthesizing sinusoids. A second-order digital resonator by the impulse-invariant transform (IIT) is applied to generate deterministic components and the results are band-pass filtered to adjust magnitude. The noise is calculated by first generating the sinusoids with formant synthesis, subtracting them from the original sound, and then removing some harmonics remained. A line-segment approximation is used to model noise components. The synthesized sounds are consequently by adding sinusoids, which are shown to be similar to the original haegeum sounds.