Noise reduction via harmonic estimation in Gaussian and non-Gaussian environments

In this paper we have presented an online method for denoising non-stationary signals in a non-Gaussian environment using particle filters. In this method we extract (estimate) the signal time-varying harmonics from noisy observations and we reconstruct (denoise) the signal from estimated harmonics. We utilize two different state-space models for estimation, one based on Fourier coefficients and the other based on Gabor coefficients. We show that Fourier based model can only handle stationary/mildly non-stationary signals. We derive the latter using block-recursive Gabor transform. Using Gabor based model, we address the problem of estimating time varying harmonics of a quasi-periodic signal corrupted by a statistically known noise. The Gabor based model provides a multiresolution approach to solve this problem. We test our algorithm with two quasi-periodic signals and we compare the results with the results of wavelet denoising method.