For a step function (X = 1) and a = 0.5, the output of the first filter should be

1, 1.5, 1.75, 1.875, 1.9375 and so on (the gain of the filter is 1 / (1 - a), which needs to be corrected after the filter, but taken into account in order to avoid overflow).

For the second one (a = 0.5), it should be

0.5, 1.25, 1.625, 1.8125, 1.90625, etc.

That is, unless I forgot my math due to caffeine deprivation (it's Sunday, and I'm trying to limit my intake of the stuff on the weekends (without too much success, unfortunately)). Also, it's been a while since I've done this without the help of MatLab.