A AM/FM Single Component Signal Reconstruction using a Nonsequential Time Segmentation and Polynomial Modeling

Overview & Synopsis

The problem of estimating nonstationary signals has been considered in many previous publications. In this paper we propose an alternative algorithm in order to accurately estimate AM/FM1 signals. Only single component signals are considered. We perform local polynomial modeling on short time segments using a nonsequential strategy. The degree of polynomial approximation is limited due to the shortness of each time segment. The time support of a segment is controlled by a criterion defined on the spectrogram. To keep optimality a maximum likelihood procedure estimates the local model parameters leading to a non linear equation system in R7. This is solved by a Simulated Annealing technique. Finally, the local polynomial models are merged to reconstruct the entire signal model. The proposed algorithm enables highly nonlinear AM/FM estimation and shows robustness even when Signal to Noise Ratio (SNR) is low. The appropriate Cramer Rao Bounds (CRB) are presented for both polynomial phase and amplitude signals. Monte Carlo simulations show that the proposed algorithm performs well. Finally, our proposed method is illustrated using both numerical simulations and a real signal of whale sound.