The paper presents a spectral representation for general type two-sided discrete time signals from $\ell_\infty$, i.e for all bounded discrete time signals, including signals that do not vanish at $\pm\infty$. This representation allows to extend on the general type signals from $\ell_\infty$ the notions of transfer functions, spectrum gaps, and filters, and to obtain some frequency conditions of predictability and data recoverability.

翻译：本文针对$\ell_\infty$中的一般类型双边离散时间信号（即所有有界离散时间信号，包括在$\pm\infty$处不衰减的信号）提出了一种谱表示。该表示能够将传递函数、频谱间隙和滤波器等概念推广至$\ell_\infty$中的一般类型信号，并得到可预测性与数据可恢复性的一些频率条件。