In practical engineering applications, useful information is often submerged in strong noise and the feature information is difficult to be extracted. Aimed at the detection problem of multi-frequency signal under colored noise background, a novel weak signal detection method based on stochastic resonance (SR) tuning by multi-scale noise is proposed. Firstly, noisy signal is processed by orthog...

We consider strong uniqueness and thus also existence of strong solutions for the stochastic heat equation with a multiplicative colored noise term. Here, the noise is white in time and colored in q dimensional space (q ≥ 1) with a singular correlation kernel. The noise coefficient is Hölder continuous in the solution. We discuss improvements of the sufficient conditions obtained in Mytnik, Per...

In this paper, we propose a single-channel speech enhancement method in terms of subspace techniques to reduce the noises from speech signals in various noises environment. This subspace approach based on Karhunen-Loève transform and implemented via Principal component analysis. The optimal subspace selection is provided by a minimum description length criterion. An offset factor generated from...

The response properties of excitable systems driven by colored noise are of great interest, but are usually mathematically only accessible via approximations. For this reason, dichotomous noise, a rare example of a colored noise leading often to analytically tractable problems, has been extensively used in the study of stochastic systems. Here, we calculate exact expressions for the power spect...

We consider stochastic inflation coarse-grained using a general class of exponential filters. Such coarse-graining prescription gives rise to inflaton-Langevin equations sourced by colored noise that is correlated in $e$-fold time. The dynamics are studied first slow-roll for simple potentials first-order perturbative, semi-analytical calculations which later compared numerical simulations. Sub...

The problem of frequency estimation a single sinusoid observed in colored noise is addressed. Our estimator based on the operation sinusoidal digital phase-locked loop (SDPLL) which carries information its phase error after noisy has been acquired by SDPLL. We show computer simulations that this beats Cramer-Rao bound (CRB) variance for moderate and high SNRs when general low-pass filtered (LPF...