Estimation of Instantaneous Frequency and Amplitude of Multi-Component Signals Using Sparse Modeling of Signal Innovation

This paper introduces a new method for estimating modes in non-stationary mixture signals. First, we establish a connection between the short-time Fourier transform (STFT) and sparse sampling theory, representing observations as pulses filtered by a known function. Leveraging the finite rate of innovation in the target signal, our specialized reconstruction approach enables mode estimation amidst noise. Second, we propose a variant based on a recursive version of the STFT allowing real-time mode parameter estimation with sequential acquisition. We compare our results with state-of-the-art methods, showing an improvement in estimation performance across various scenarios. Our approach paves the way of the future mode disentangling algorithms based on Finite rate of innovation.