An Adaptive Denoising Algorithm for Improving Frequency Estimation and Tracking

We propose a novel adaptive denoising algorithm which, in presence of high levels of noise, significantly improves super-resolution and noise robustness of standard frequency estimation algorithms, such as (root-)MUSIC and ESPRIT. During the course of its operation, the algorithm dynamically estimates the power spectral density of noise and adapts to it. In addition, the proposed denoising front-end allows signal samples to be non-uniform, enabling the standard frequency estimation algorithms to achieve the same super-resolution, accuracy and noise robustness for non-uniformly sampled signals as for uniformly sampled signals of the same sample density. Extensive numerical tests verify superior denoising performance compared to the standard Cadzow method, especially when the noise present is not white. Our algorithm exploits salient features of numerically robust differential operators known as chromatic derivatives and the associated chromatic approximations which provide a method for digital processing of continuous time signals superior to processing which operates directly on their discrete samples.