EXTRAPOLATING ESTIMATION OF BAND-LIMITED FUNCTIONS IN GAUSSIAN WHITE NOISE

Suppose f(t) is a σ-band limited function and g(t)=f(t)+n(t) is observed in the interval （-T,T）, wheren(t) is a Gaussian white noise. The maximum likelihood estimation of f(t) based on g(t) is presented in this paper. It is also discussed that the estimation minimizes the mean square distance to g(t) when f(t) is a random σ-bandlimited function.