Sampling Theorem and interpolation formula for non-vanishing signals

The paper establishes frequency predictability criteria and presents predictors for two-sided non-vanishing bounded continuous time signals, i.e., for signals from L∞() that do not necessarily vanish at ±∞. The notions of transfer functions, the spectrum gaps, bandlimitness, and high-pass filters are introduced for these signals. This allowed to obtain an analog Whittaker-Shannon-Kotelnikov sampling theorem and a new modification of the corresponding interpolation formula that makes it applicable for non-vanishing signals.