It depends on what what a continuous spectrum is defined as. In the case of a single atom, when an electron absorbs energy, it jumps to a higher orbital. An electron in an excited state can release energy and ‘fall’ to a lower state. When it does, the electron releases only one photon of electromagnetic energy per energy level dropped per atom. If there are multitudes of atoms, it can be seen a pulse, or beam. In the case of a spectrum, generally, the type of element dictates the color that the photon emits.