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.
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