Rising and Falling Edge non-monotonic detection possible?

hi everyone, i was wondering if it is possible to use matlab to automatically detect the non monotonic value (change in y value, dy) as shown in the following diagram.

http://imageshack.us/photo/my-images/638/3247siam3505.jpg/

 The diagram was taken as it has the best illustration of what i'm trying to achieve but one note is that i have a random sequence data which consists of multiple pulses (eg: 16 bits of data per sequence) of similar shape as shown in the picture (basically they all have non-monotonic which i am required to measure)...is it possible to do so? i was thinking of differentiating and finding the turning points of the entire waveform and begin measuring from each turning point but one problem is that there is ripple at the stabilized section of the waveform which will cause false alarm or incorrect calculation. for rising edge section, i need to get the drooping part (shown in the diagram above) whereas for falling edge section i need to measure the increasing part (shown in the diagram below-labelled with "2" without the quotes) hence this requires me to be able to distinguish between the rising and falling edges of the pulses.

http://imageshack.us/photo/my-images/808/72481145.png/

my main aim is that i have to measure the worst non monotonic value in both the rising edge and falling edges of all random data bit waveforms.

this is a challenging assignment which i have been working for weeks to no avail...any help or tips from experts would be greatly appreciated! thanx!:)