I'm an Electrical Engineer. Graduated many years ago...

What you are looking for is a 2 step process...

First you would need a differential/comparitor circuit. Then use DC biasing to distinguish the positive rising slope as opposed to the negative decreasing slope....

Of course there are many ways to skin a cat....

Another way is using a one shot multi-vibrator IC and have it edge triggered either positively or negatively. That would capture only the leading or trailing edge of the signal you want to process or filter...

You can also use inverters to change the direction of the sawtooth wave, if need be....

The main problem would be frequency of the sawtooth wave. The circuits that I described above will work on slower frequencies. Very fast frequencies would be a little more intricate to build....