AbstractA general form of sampling theorem is considered in which the signal is uniquely interpolated by sample values taken at a number of uniformly spaced sample points for a band‐limited time function of the form f(t) such that ∫−∞∞|f(t)|2dt<+∞ and whose Fourier spectrum contains components within |ω|<ω0. One of the necessary and sufficient conditions establishing such an interpolation function is derived. According to the theorem, this interpolation function can be given in terms of time functions that correspond to the coefficients obtained by Fourier series expansion with respect to a function of angular frequency and time, called the generating function. Next, for a signal of the same form considering a generalized form of the sampling theorem that deals with nonuniform sampling points, the necessary and sufficient condition for the interpolation function that ordinarily establishes this is shown. In this case it is also shown that the concept of the generating function can be extended. Further, by combining the well‐known Silverman‐Toeplitz theorem for summation of series and the sampling theorem as derived above from the outline of the generating function, several sampling theore