Power electronic devices are inherently discontinuous systems. Square waves, produced by interconnected transistors, are commonly used to control inverters. This paper proposes a novel phasor transform, based on the theory of moments, which allows to analyze the steady-state behavior of discontinuous power electronic devices in closed-form, i.e. without approximations. In the first part of the paper it is shown that the phasors of an electric circuit are the moments on the imaginary axis of the linear system describing the circuit. Exploiting this observation, in the second part of the paper, we focus on the analysis of circuits powered by discontinuous sources. The new “discontinuous phasor transform” is defined and the v-i characteristics for inductors, capacitors and resistors are described in terms of this new phasor transform. Since the new quantities maintain their physical meaning, the instantaneous power and average power can be computed in the phasor domain. The analytic potential of the new tool is illustrated studying the steady-state response of power inverters and of wireless power transfer systems with non-ideal switches.