Spectral Representation of Two-Sided Signals from \(\ell_\infty\) and Applications to Signal Processing

We study spectral representation as well as predictability and recoverability problems for nonvanishing discrete-time signals from $\ell_\infty$ , i.e., for bounded discrete-time signals, including signals that do not vanish at $\pm\infty$ . We extend the notions of transfer functions, the spectrum gaps, bandlimitness, and filters to these general type signals. We present some frequency conditions for predictability and data recoverability and propose some prediction and data recovery methods.