ANALYTIC SAMPLING APPROXIMATION BY PROJECTION OPERATOR WITH APPLICATION IN DECOMPOSITION OF INSTANTANEOUS FREQUENCY

摘要

A sequence of special functions in Hardy space H~2(T~s) 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 H~2(T~s). That is, f can be approximated by its analytic samples in D~s. Under a mild condition, f is approximated exponentially by its analytic samples. By the analytic sampling approximation, a signal in H~2(T) can be approximately decomposed into components of positive instantaneous frequency. Using circular Hilbert transform, we apply the approximation scheme in H~s(T~s) to L~s(T~2) such that a signal in L~s(T~2) can be approximated by its analytic samples on C~s. A numerical experiment is carried out to illustrate our results.