Double series representation of bounded signals

Series representations of the form f(t) approximately Sigma /sub n=- infinity //sup infinity / Sigma /sub k=- infinity //sup infinity /a/sub n,k/ nu (t-n)/sub e//sup 2 pi /kts/ for bounded signals f(t) are studied, as are conditions on the unit function nu (t), such that coefficients a/sub n,k/ reveal the energy content of f(t) in the time interval n-(1/2)<or=t<or=n+(1/2) and frequency interval 2 pi (k-(1/2))<or= omega <or=2 pi (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.<<ETX>>