Double series representation of bounded signals

Series representations of the form f(t)~Σ_n=-∞^∞Σ _k=-∞^∞a_n,kν(t-n)_e ^2πkts/ for bounded signals f(t) are studied, as are conditions on the unit function ν(t), such that coefficients a_n,k reveal the energy content of f(t) in the time interval n-(1/2)⩽t⩽n+(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