Joe, it's good to solve a problem by breaking it down into it's different elements. Also it's important to specify your requirements as clearly as possible.
Reading this I
assume that you are wanting the picaxe to output an
exact replica of the two incoming pulses (ie the pulse widths are the same, the time between the pulses are the same) but delay this output by a variable time delay.
So there are two parts to this problem:
1. Picaxe 'recording' received pulses
How can a picaxe detect a pulse? Well, it depends on how fast you mean by fast pulses. There are two options I can see:
a) the pulsin command that can be used to detect relatively fast pulses. Or
b) you can just monitor the input pin using code and wait for the digital state of the input to change.
There are potential issues with both options, and it hinges on your requirements. For instance, if the pulses are too fast then b) might not work because the code might not be quick enough to detect the transitions. But with a) there might be a problem with measuring the time
between pulses.
Also, there are diffrent ways of recording the pulses. Pulsin measures the pulsewidth of an incoming pulse, so if you went this route you would be measuring the widths of the pulses and the gap between the pulses.
You could do the same with approach b). However I can also see another option, and that's to take a stream of regular samples of the input pin.
2. Picaxe 'playing back' a delayed replica of the pulses
Well the first thing is to delay. What command does the picaxe use to delay?
Then the playback depends on what solution you used in 1.
I'm not going to give code because I think you need to look at the different elements, clarify your requirements, looking at the different design options, chew over the pro's and con's of each option.
Learning how to approach problems is a valuable skill