  Semiconductor heterostructures with prescribed energy dependence of the
transmittance can be designed by combining: {\em a)} Pad\'e approximant
reconstruction of the S-matrix; {\em b)} inverse scattering theory for
Schro\"dinger's equation; {\em c)} a unitary transformation which takes into
account the variable mass effects. The resultant continuous concentration
profile can be digitized into an easily realizable rectangular-wells structure.
For illustration, we give the specifications of a 2 narrow band-pass 12 layer
$Al_cGa_{1-c}As$ filter with the high energy peak more than {\em twice
narrower} than the other.
