Question

. Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = 365+1096+4) (.e. f(t) is causal) lim f(t) = 00 1-0 limf(t) = 1. 10x4 lim f(t) = 0 • limf(t) cannot computed since sF(s) is not analytic. None of these choices is correct. -0 . t-0 t+0 . b) (2 points) What is the final value of time function f(t) corresponding to the one 40 sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10) (s2+4) lim f(t) = 0 40 lim ft) 1. 10 x 4 lim f(t) 0 lim f(t) cannot be computed since sF(s) is not analytic. None of these choices is correct . c) (1 points) If the ROC is to the right of the right most pole of a transfer function then the transfer function represents a causal system. (true) (false) (correct answer not given)

Answer 1

that Solution)a) We are given F(s) - До we mowo !! 2 have to calculate $ (SFv) (4) initial value of f(ts. from value theoren initial thus lim S.F(s) [ initial value 416) w theorem S→0 lim atting $ x 40 $> 8 (stio) (s²th [Rut S = ودیو = O this lim f(t) О Ang tto that b ) We are given (s) = 4 o Now, we s(s+10)(8+4) need to calculate the final value in time function. This from final value f(0) = Cim f(t) = lim S F() theorem . ta sto [ final value theasem

Thus we از مواد اور امارات get lim f(t) = lim8 x 40 +-700 sno s(s+10) (s%+4) 5 I - lim 40 sto (stio) (5²74 Ho Joxy D - this lim f(t) = 40 Ane too 10x4 c ) system is a ROC TRUE Explanation If an LT! system Causal one then it's of H(s) is on to the right sided half plane In other words of H(s) is equal to N/5)/0 (3) then for causal system ROC lies to the the sightmost pole and order of NCS is not more than D(s). Right of
summary - thus all the required values were calculated out with correct explanation of the used formula and explanation was provided.