A formerly common use for Transductors was in CRT displays, to correct a distortion called pincushion distortion, where the side of the picture bowed in at the centre as a result of the geometry of large deflection angles.
It would have one set of windings in the horizontal deflection circuit and the other set in the vertical; the action of the transductor caused the deflection waveforms to modulate each other - reducing line scan at the top and bottom (where the magnetization from the vertical deflection waveform was greatest) and similarly on the vertical waveform (where the magnetization from horizontal scan current was greatest).
[1] An additional use for the transductor, prior to Hall effect devices, was as a feedback transducer for large dc current measurement.
The dc bus to be measured passed through the center of the toroidal iron core saturable reactor and 120vac excitation was applied to the winding around the iron core.
In this manner, dc currents of 30,000 amps or more could be accurately measured without electrically bonding to the bus.