Question

I need to prove and identify is the system fulfill the following characteristics (part 1 to part 4)?

yn] =n2x[n +1]

part 1: is it linear?

part 2: is it BIBO stable?

part 3: is it causal?

part 4: is it time invariant?

Answer 1

Ylm) = n² al-n+1) Part (1) all) I Yn) = ² x 1-n+1) 0,,1m) +QnRy in) Ivylm) = 0,max(-+) ta, max (-741) il silm I vm) , in I (1) 9,, (m) + QxY, IM) = aina y(-m +1) + ann? x (=m+1) (11 equation 0 8 D equal hence it is linear Part 2 il bounded input Bounded output (BIBO) then stable el Bounded input umbounded ow put them unstable ich input is bounded input xnl is xl-n+1) and suput ylm) relation Min)=hm) x(m) => x[k) hink) k=- Now tirst definite sequence A discret time sequence is said to bounded if the absoulute value od element is less than some timit number this will be bounded il kelnl is less than intinit \x{nco Now absolute volue of ym. number Tym elke \-*43) E-

Tym = 5 1K 12 = 0 KE- / unbounded output) not tinit summation hence system is unstable Part 3 Ylm = nhat-n+1) not causal because output value depend on future. and past Value of imput X (-1), X12), X1-1), X(-2) e Past tuture Part 4) Y(n) = x1-n+1) It no delay by input antalon-notl) = mxl-m-no+1) 0 second no delay by output =y\n-nol = (n-noful-In-Not) = (m-m.)?xl-n+Noti) - equation 07 (11 not time mvariant LORS time variant