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Double series representation of bounded signals

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3 Author(s)
Jensen, H.E. ; Math. Inst., Tech. Univ. of Denmark, Lyngby, Denmark ; Hoholdt, T. ; Justesen, J.

Series representations of the form f(t)~Σn=-∞Σ k=-∞an,kν(t-n)e kts/ for bounded signals f(t) are studied, as are conditions on the unit function ν(t), such that coefficients an,k reveal the energy content of f(t) in the time interval n-(1/2)⩽tn+(1/2) and frequency interval 2π(k-(1/2))⩽ω⩽2π(k+(1/2)). These conditions turn out to be orthogonality and integrability. Based on these conditions a number of properties of the expansion are derived, including summability of the double series and energy and power estimations. Some examples of the expansion are presented

Published in:

Information Theory, IEEE Transactions on  (Volume:34 ,  Issue: 4 )