On Local Chirp Rate Estimation in Noisy Multicomponent Signals: With an Application to Mode Reconstruction

In this paper, our goal is to investigate local chirp rate (CR) estimation in noisy multicomponent signals. The focus is put on improving a specific type of local CR estimator used in the second order synchrosqueezing transform, which proves to be very inaccurate in the presence of noise. More precisely, the noise creates spurious oscillations in the local CR estimate, and we first put the emphasis on the terms responsible for these oscillations. Then we propose a novel technique to filter them out, resulting in a much more accurate local CR estimator. We finally show how to use the latter to improve mode reconstruction and investigate in what way the new CR estimator is useful in the context of voice signals.