I. Introduction
The classical sampling theorem [1]–[3] has a constructive nature since it shows the ways of representing a bandlimited signal with bandwidth B by its samples (or by the samples of its function ) and determines sampling and interpolation algorithms and circuits optimal in the least-squares (LS) sense [4]. Here, / is a sampling period and fs is a sampling rate. The interpolation equations are included in the theorem’s statements. The sampling algorithms and circuits follow from the fact that sampling is an expansion of by the generalized Fourier series with respect to the set of sampling functions [4]. The minimum rms errors of such series are achieved when samples , which are their coefficients, are calculated as \begin{equation*}u(nT_{s})=\displaystyle \frac{1}{\Vert\varphi_{n}(t)\Vert^{2}}\int_{-\infty}^{\infty}u(t)^{*}\varphi_{n}(t)dt\tag{1}\end{equation*}