We report an analytical theory of linear emission of exchange spin waves from a Bloch domain wall, excited by a uniform microwave magnetic field. The problem is reduced to a one-dimensional Schrödinger-like equation with a Pöschl-Teller potential and a driving term of the same profile. The emission of plane spin waves is observed at excitation frequencies above a threshold value, as a result of a linear process. The height-to-width aspect ratio of the Pöschl-Teller profile for a domain wall is found to correspond to a local maximum of the emission efficiency. Furthermore, for a tailored Pöschl-Teller potential with a variable aspect ratio, particular values of the latter can lead to enhanced or even completely suppressed emission.