Consider a discrete time rectangular pulse signal $[]=[][]$ where $<.$

Student A states that the region of convergence of $[]$ must always be the entire $$ plane, excluding

the point $=0.$ Student B is correct in disagreeing with Student A$.$ Why?

$2.$ For an asymptotically stable and causal system, we know that the characteristic modes must decay

to $0$ as time goes to $.$ Student A states that it is possible for the poles of the system to have real

parts that are positive. Student B disagrees and asserts that the poles of the system must always have

real parts that are negative. Who is correct and why?

$3.$ When determining the system transfer function $()($or $[])$ of an LTIC $($or LTID$)$ system, we

ignore the initial conditions. A student is then confused as to how you obtain the total output

response $()($or $[])$ from the system: where do the initial conditions come in$?$ How can you

help resolve the student$$s confusion?