Abstract

Communicated by (xxxxxxxxxx) A sequence of special functions in Hardy space H2(Ts) are constructed from Cauchy kernel on unit disk D. Applying projection operator of the sequence of functions leads to an analytic sampling approximation to f, any given function in H2(Ts). That is, f can be approximated by its analytic samples in Ds. Under a mild condition, f is approxi-mated exponentially by its analytic samples. By the analytic sampling approximation, a signal in H2(T) can be approximately decomposed into components of positive instanta-neous frequency. Using circular Hilbert transform, we apply the approximation scheme in Hs(Ts) to Ls(T2) such that a signal in Ls(T2) can be approximated by its analytic samples on Cs. A numerical experiment is carried out to illustrate our results.