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Localization operator and digital communication capacity of channel

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  • In mathematical language, the communication model of some digital information channel can be described as the self-adjoint operator $Q_T P_\Omega Q_T$ on $L^2(R)$, where $T$ and $\Omega$ are constants. $T$ is called signal peroid and $\Omega$ is called channel's bandwidth. By computing the eigenvalues and the corresponding eigenfunctions of the compact self-adjoint operator $Q_T P_\Omega Q_T$, the conclusion of Landau, Pollak and Slepian shows that about $2\Omega T$ bits data can be transmitted by this channel within time $T$ when $\Omega T$ is sufficiently large. Considering the realistic communication model, this paper points out that in one signal period $T$, at most $2r\Omega T$ can be transmitted with $r$ ($r\in (0,1)$) dependent on some given threshold $\eta $.

    Mathematics Subject Classification: Primary: 47B32, 47A75; Secondary: 42C40, 94A40.


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