Its should be a standard irDA setup. Here's a good article on how it works: [http://www.societyofrobots.com/electronics_irda_tutorial.shtml|IrDA Transceiver (Infrared Transmitter Tutorial)]
What you'll want to do here is make a tool to 'see' the IR signal. Here is a simple set of circuits which you can build to test the IR signal and with it you should also be able to measure the signal with a few modifications: [http://fritzing.org/projects/infrared-based-music-transmitter-and-receiver|Infrared based music transmitter and receiver].
In your case you'll need to modify the speaker output so it can be connected to your computer as an audio input then saving the output into an audio file which you can open up within an app to measure the time base of the signal.
A coworker of mine a few years ago did this so he could control a TV set for his mother who had a hard time changing channels using the TV remote (she has arthritis and was bed ridden). In his case he programed an iPad so each station was a single button she could press. He used this IR unit [http://www.engadget.com/2010/03/02/redeye-mini-converts-iphone-ipad-or-ipod-touch-into-ir-beaming/|RedEye]. At the time it was a novel idea. Today there are quite a few IR and even TCP/IP over WiFi or Ethernet that can do this.