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

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 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 stated in terms of the generalized frequency. The bound for truncation error of the generalized sampling expansion is briefly mentioned.