The DX-4D has a 6-pin "control signal" connector on the back as well as the RCA ins and outs. You need to have an input connector for this on your tape deck. It would be marked "DBX unit control signal".
I'm not sure if a Model 52 has such a connection.
I believe the DX-2D has a similar connector, the only difference probably being 4 channels of noise reduction vs. 2 on the DX-2D.
The "control signal" connection serves to switch between encode/decode of the DX unit automatically, during recording or playback. It won't work at all if there is no such connection on the 52.
If the 52 doesn't have it, you may have to go with a used
DBX-150X unit. That has 2 channels of noise reduction, record/play switching on the front, and 1/4" TRS connectors to the deck and console. (ugh, more adapters) Info on the unit is still on the DBX website, though it is discontinued.
Another option may be the older
DBX-150. It used RCA connectors for the deck and console. That was made when DBX was in Newton, MA.
All the above units are DBX Type 1 noise reduction.