The paper studies spectral representation as well as predictability and recoverability problems for non-vanishing discrete time signals from $\ell_\infty$, i.e. for bounded discrete time signals, including signals that do not vanish at $\pm\infty$. The extends the notions of transfer functions, the spectrum gaps, bandlimitness, and filters, on these general type signals. Some frequency conditions of predictability and data recoverability are presented, and some recovery methods and predictors have been suggested.

翻译：本文研究了$\ell_\infty$中非消失离散时间信号（即有界离散时间信号，包括在$\pm\infty$处不消失的信号）的谱表示以及可预测性和可恢复性问题。本文将传递函数、谱间隙、带限性和滤波器等概念推广到这类广义信号上。文中给出了可预测性和数据可恢复性的一些频率条件，并提出了一些恢复方法和预测器。