2024/09/12 by Nikolai Dokuchaev, Dokuchaev, Nikolai
Mathematics · Computer Science · #Mathematical Analysis and Transform Methods #Image and Signal Denoising Methods
paper · pdf · doi:10.48550/arxiv.2410.03667
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 kth coefficients of this formula is ∼ 1/k2. 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.