  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 Schr\"odinger-like equation with a
P\"oschl-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
P\"oschl-Teller profile for a domain wall is found to correspond to a local
maximum of the emission efficiency. Furthermore, for a tailored P\"oschl-Teller
potential with a variable aspect ratio, particular values of the latter can
lead to enhanced or even completely suppressed emission.
