A simple resistor won't do it....

You'll need an RC differentiator feeding a zero crossing detector.

The differentiator will convert the one long positive pulse into 2 pulses at the transitions, the first will be positive, and the second negative.
The ZCD will give a positive pulse each time that signal hits zero.

Unfortunately it's not a simple mug-handed solder job - you'd need to be comfortable with laying out a circuit on perfboard... ?