Hayashi, Y., 1976: Non-singular resonance of equatorial waves under the radiation condition. Journal of the Atmospheric Sciences, 33 (2), 183-201.

Abstract: A response of large-scale equatorial waves to a thermal or a lateral forcing confined in the troposphere is examined analytically by imposing the radiation condition based on an equatorial beta-plane model without wind shear.
A resonant response with large finite amplitude occurs under the radiation condition, when the vertical scale of the wave coincides with that of the forcing. This "non-singular resonance" is associated with a sharp spectral peak for equatorial waves which are characterized by a small variation of the frequency with the vertical wavenumber. However, such resonant equatorial waves are not realistic, since their vertical velocity is not in phase with the imposed convective heating and their pressure is not in geostrophic balance with the meridional wind of the imposed mid-latitude disturbances.
This study suggests that the forcing cannot be imposed arbitrarily regardless of its feedback. It assures on the other hand that the equatorial waves simulated by a general circulation model are not spurious resonant waves resulting from an artificial reflection at the top of a finite-difference model.