Sampling Theorem and explicit interpolation formula for non-decaying unbounded signals (2410.03667v5)

Abstract: The paper establishes an analog Whittaker-Shannon-Kotelnikov sampling theorem for unbounded non-decaying band-limited signals. An explicit interpolation formula is obtained for signals sublinear growth with rate of growth less than 1/2. At any time, the rate of decay for the $k$th coefficients of this formula is $\sim 1/k^2$. In addition, the paper obtains a method for calculating the coefficients of the interpolation formula applicable to signals with arbitrarily high rate of polynomial growth.