What is the time interval for which y 13 nonzero Is the syst

What is the time interval for which y 13 nonzero? Is the system casual? Why? Is the system bonded input bonded output stable? why?

Solution

a.) when x(t) gets multiply with h(t) the time interval from -4 to -1 will become zero as h(t) is zero from -4 to -1.so as result in multiplication it will give zero from -4 to -1.similarly from interval 2 to 3 h(t) again zero which gives zero when multiply with x(t) from 2 to 3.and from -infite to -4 and 3 to infinite both functions are zero so output will be zero in this interval.hence it will give non zero value from interval -1 to 2.

b) System is non causal .for system to be causal it only depends on present and future value but given function also depend on negative value of time ,So this sysytem is non-causal.

c) yes,this sysytem follow BIBO(bounded input bounded output ) stable.for every finite value of input(bounded input) there exist a finite output(bounded output) i.e. for non infinte input output is always non finite,it always give a finite output.So it is BIBO stable.