Question

Q2) For the following system with response: ht[n] = " a[n] where a is a constant, a) Is this system causal? Why? b) is the system stable? Why? Repeat a) and b) for: h2[n] = en u[n] h3[n] = a" u[n +4]

Answer 1

# Guven 0 Lin-au [N] haln=eu in) Whs n) = [n+9) We have to find the given systems are a 0 Causal ① Stable © Eausal Systeng :-* We called a system lausel wif the output of system uš rindependent of fecture value of Vinput tten system is called lausa.. • Metamobally; *[r]=0 fox nko Stable System : A System is said to be stable if ita autput should be bounded for bounded input (finite In Amplitude). [ Ihn]I <a » Finite Value olide 8=-2 del can 6 Le [n] = am En from the given system say ittal ttat hin=0 for no. Som h, [n] is causal system. Thi(n)=0; for no] =D AS un] starts from o. purn

4 for Stability Žaw, Elhony = [lahu (n) | のこ-8 nad Elanl no E a no 3 e alta tata? t So, we are met getting froute value. Ses It is nat stable. he [m] = au in for the given system say lat ha en 720 ; no. So, hz [n] W Caual System due can (# [the(n) | Elemen/ nap =ł len nzo E en no = et etter ha [n] is nost stable So, we are met getting fruite value. Jo,

M[nte Oh (n) = 6" M [n+0] ho 7+9=0; 03-4 -47-340123 Son lle can I say that that h3 [n] to g for no Hence, hs [n] is a Nat Gused System [ Ihz (n] Epe [n+4) h=-d hip == la" Š n=-4 - -1 a ta ta ta ta ta tat a So, we are not getting a firuite value. Hence to [m] û e Not a stabile Sistem Constable System) - Causal Unstable. hen? Į Unstable - Causal ha (o -I Unstable Ang - Non-Causal hy ) Unstable
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