Decide what exact length of time makes a wide pulse. When a pulse begins, wait for that length of time, to see if a pulse drops back to 0V before the time window closes.
If it is still high at the end of that time window, then you do not send a pulse. Otherwise you send a pulse.
It may be possible to configure a 555 timer IC to do the job.
For my space requirements, a 555 timer is way to big a block to solve this problem. I was thinking of just putting something like a series capacitor which would allow the short pulses to pass through (cause its almost an high frequency ac signal) and block the wide width pulse (cause it's like a DC signal) Is this method correct/feasible?
It doesn't work this way. The edges of the wide pulse contain the same high frequent signal components as the small pulse.
Firstly your problem specification is "way too" vague. I understand that you intend a pulse by pulse filtering rather than presence detection of a fast pulse train. Pulse by pulse detection requires a time filter that actually measures pulse width. Must not necessarily use a 555 timer, but at least RC circuits with logic gates that regenerate a digital waveform.
Secondly, I suggest to elaborate your detection algorithm. Obviously, a small pulse can't be recognized before the falling edge occurs. Deciding to pass the pulse a this time isn't possible, the only way is to replicate a (delayed) small pulse when the falling edge occured.
It turns out that there not two different pulse widths rather than a continuous pulse width range, I guess with a constant pulse period.I have two different type of digital pulses flowing out of a gate.