How to re-generate a previously saved SIRC protocol waveform?
Since I do not have "Comment" privileges, I'm responding in Answer form, though this is not an answer:


Are you sure your IR LED is connected to the base of the transistor as you state, and not like the first schematic on this page? 
Is the IR LED you are using, of the same IR wavelength as is expected by the TSOP1738, i.e. 950 nanometer or therabouts?


Possible answer:
Your oscilloscope trace of the Arduino generated signal shows a PWM frequency of 39.215 KHz, and the final signal trace shows effects typical of aliasing between two windows of slightly different frequencies. Try getting your output closer to the nominal 38KHz, and recapture results for this discussion, please.

[Edit: Woohoo, I just received "Comment anywhere" privileges! So I'll leave this answer in place and amend it towards a valid answer if I can.]