Estimating the period of a signal of unknown shape corrupted by white noise
Consider a stochastic process x(t) observed on the time interval [- T/2,T/2]. The observed process is the sum of an unknown periodic signal s(t) and white Gaussian noise n(t) of unit spectral density, \[ (1)\quad x(t)=s(t)+n(t),\quad t\in [-T/2,T/2]. \] Given the observations x(t), it is required to estimate the period \(\tau_ s\) of the signal s(t). The bounds \((\alpha_ T,\beta_ T)\) on the possible values of the period \(\tau_ s\) are assumed known. We consider this statistical problem in an asymptotic setting, assuming a sufficiently long observation time T.
scientific article; zbMATH DE number 4109906