I'm doing a thing in signal analysis, and in order to get the impulse response of a system, i have to convolute the impulse responses of its components. This is what i came up with: Task a and b
The answer in a looks fine to me at first, but when i do b, proving that the system is BIBO stable (Bounded input, bounded output) I do it by proving that both of the subsystems are BIBO (which i THINK is a valid property). However, that would mean that i have done something wrong on task a (im guessing around line 3 or 4 from the bottom) as i can't seem to get this to converge. What have i done wrong