It is the noise of the data when the system is granting the channel. Try adjusting the EDACS unmute timer so that it does not unmute until the channel is actually granted and you don't hear that data burst anymore. It sounds like the timer is set too low if you are getting it with every transmission. Try 16 or 18 as a default and then go from there. 16 works great with my local EDACS system. Anything lower causes the noise to be heard with every transmission or channel grant. Of course, this is on my PRO-106 and PSR-310. Haven't had to mess with it on my BC346XT as I never hear it. Unless, that is, the longer burst occurs.
The longer bursts, I think, are usually caused by a busy system trying to find an available channel to grant the communication to. The actual radio user hears a low tone, meaning there is no access to an available channel and the radio is not transmitting, until the channel is granted. Scanners, unfortunately, just receive the data bursts until the channel is granted. This is more noticeable on the sites that have the smaller channel capacity and a high volume of calls. Even if you change the EDACS unmute timer to a longer time, you may still hear an occasional long burst.
If any part of this is wrong, please feel free to correct me. I am not an EDACS TRS sysop so it may be wrong. I just know that I get the same noise at the beginning of each transmission if I set my EDACS unmute time at a low setting. I try to get the length where the scanner unmutes just after the short burst is gone so all you get is the actual comm and not the data burst.