On the Generalized Sampling Theorem, Generalized Frequency, and Generalized Band-Limited Spectrum Function

瀧澤英一(Eiiti Takizawa)

Chinese Journal of Physics

13卷2期（1975 / 10 / 01）

226 - 246

英文

A generalized sampling theorem is presented, by which a continuous function can be reconstructed from its sampled values and sampled higher order derivatives. Several remarks are also made on the generalized sampling formula presented here. The generalized frequency and the generalized band-limited spectrum function are discussed in relation to the generalized sampling theorem. The condition for establishing the generalized sampling theorem is also stated in terms of the generalized frequency. The bound for truncation error of the generalized sampling expansion is briefly mentioned.