Question

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5. Determine whether the following LTI systems, whose impulse responses given below, are i) Memoryless ii) causal iii) stable systems. Justify your answers. (15 points) a. h[n] =(n-1)u[n] b. h[n]=a[n+4] - u[n-4] c. h[n] = (0.2)"u[-n]

Answer 1

a ) O L bin) =(n-1) 0(0) Put no h10) = (0-1) ulo) Here we can see the system depends on the the present in but only. Hence the System is Memory less For cowsality b(n)= 0 Dco So we can see b[n)= f (m -- -1) for no <.0 Hence this is causal s system. bilne (n-1) un) H (2) 2 I-212-1 2-12 (21) (2-12 Here ROG IZI 7 Here Roc is outside the unit urcle Hence this is UNSTABLE SYSTEM → Memoryless - Causal Unstable system bln) = uinti) - On-4) Put n=o 6 (D)= U(1) - (--) Her blo) depends on past input (ice 0 (-u)) & futwe in put fie U (1)). Hence the system bós memory for causality t(n=0 Let's check bln) = -4<< n 4 b ) ; nco no So hot hinto Hence this is mon caw sal system for Stability 36(n) < do Let's check Šthitta- +++1+1+1+1+1+1=8 com Hence this is stable system ņe-4

Memory + Non causal, Steble c) b(b)= (0 29UZn) Put no deme system bln) defends am blusent in but lural) Hema this is memoryless (6) 0 = (ملط for causality D८0 ha=0 Let's check h(n) = Do Q 00 Hence this is causal system For stability H (2) = Roc: 270.2 2-002 Hence Roc is inside the unit corte 121=ti Hence this is stable system Z = Hemoryless, causal & Stable system
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