Page  88 ï~~Parameters estimation for non-linear I help of time-frequency analy Delprat.N, Guillemain.P, Kronland-Martinet.R. Laboratoire de M6canique et d'Acoustique du C.N.R.S et 31, Chemin Joseph Aiguier 13402 Marseille cedex 09 Abstract 0 The goal of our study is to build a estimate parameters for non-linear synthesis tech Amplitude and Phase Modulation. Using the notion o time-frequency analysis (Gabor or wavelet transforms), lead to modulation laws. Estimation of non-linear synth( been performed on instrumental sounds In this case, s, leading to a combination of additive and non-linear synth 1 Introduction a C - 4* j n

Page  89 ï~~Gabor: s(t)..e> W(t,co) time-frequency repre time-scale represen Wavelet s(t) --> S(t,a) For more information see e.g. [2]. These operations on a signal introduce redun that all the coefficients have not the same "weight". The next section discusses how to extract a l transform, corresponding to the more important values 2.2.2 Ridge extraction. We have shown that the main cot stationary points [3J A practical criteria for their identi agt, co to Gabor 0I) Wavelet. where *)represents the phase of the transforr representation, a the dilation or scale parameter, th a scale a. It can be shown [4] that these points define transform. Moreover, the phase and the modulus of th give a good estimation of the phase and amplitude of th 2.2.3 Examples A a a AA ww w ww...a A U A t A 1.. a - - - -- a

Page  90 ï~~4 Analvsis-resvnthesis of musical sounds. The study on academic F.M. and P.M. signals understand the relation between the Q-factor of the wavel We are currently testing what happens with mi from the extracted trajectories, a very interesting step. Synthesis from the ridgy We have done a resynthesis combining addil modulation and Phase Modulation) (Fig.6). theca trajectories. For each trajectory, we extract the phase mo above. The summation of each contribution (for each t done on a saxophone sound (Fig.7) and a trumpet sound quite satisfying - p