Question

Consider three systems with the following input-output relationships

6. Consider three systems with the following input-output relationships: { 4 0, odd System 1: y[n n even r[n] 10ar(n 2]3r[n - 1 System 2: yn + + System 3: yn x[3n] The interconnection diagram is at follows: System 1 System 2 System 3 Find the input-output relationship of the interconnected system. State the properties of the system (linear, stable, time invariant, memoryless, and causal).

Answer 1

odd System neven aytem 2 Syten 3 : 3n] 남고 System3 Systen 1 neven 2 -1 eren

10 x 3n - n even ' 지[을 g + 37[문-] 10

Zinearity rpresutatron is Saypten ntauta agaLn hs a dibferent intermedint the >by2(n] b 2n aa1n +bx2C0] aynby2 Cn] Systam Then the said to be lineas. |- 10a a1 (a'5-FTe -> b +ba +2 - a - ayCn) 2n) Linear System is

stablity: nis stable, utput n t 3 +2 limited ignal. i's also a Cimited yCn) is Hence Stable tenee

Casaleky We have n even A System causal and only if the actput depends upo the doesnot bture input Cndepends upom [2j Here Fiuture input System is Hence Non Causal. Memety Property i not Memorylers System e, ystem have menory be cause depends up bture it paust inputa and Time Vaiiane Paoprty git) (t) T (to)y(t-ta)(A)(n-n) then the Time Inveriant

진2] ~ 40x[문 +2] [물 -J JA - x(꿀+2-n0) +크지(을 기+) n-no 10 2- -no= -n But ou- Pu-JA ou-uJ Not Time Dnvariant so, Systim is Time Vauiant e., System i