Given a system with pole zero plot shown below and the fact that H(0) = 5 . solutions given please show steps
Posted: Thu May 05, 2022 2:15 pm
Given a system with pole zero plot shown below and the fact that
H(0) = 5 .
solutions given please show steps
0 T Ņ H(2) a) Find h[n] given that the system is causal. b) Find h[n] given that the system is stable. Solution: A First, H(z) = so H (0) = −5, hence, A= 5. Now, do long division and expand H(z) into the sum 5 (z-2)(²+¹) of terms by partial fraction expansion: 5 Sz-2 H(z)= Sz-2 5-12-¹ 1 4 -5+ ´(z−2)(z+±)¯ (1−2z¯¹)(1+½z¯`¹)¯¯¹−¾z¯'−z² = −5+ -2 1-3z¹. 1-2z a) If the system is causal, then h[n] = −58[n]+2″u[n]+4·½" u[n]. b) If the system is stable, then h[n] = −58[n]−2"u[−n−1]+4·½″ u[n]. = -1 -N
H(0) = 5 .
- Given A System With Pole Zero Plot Shown Below And The Fact That H 0 5 Solutions Given Please Show Steps 1 (67.53 KiB) Viewed 35 times
0 T Ņ H(2) a) Find h[n] given that the system is causal. b) Find h[n] given that the system is stable. Solution: A First, H(z) = so H (0) = −5, hence, A= 5. Now, do long division and expand H(z) into the sum 5 (z-2)(²+¹) of terms by partial fraction expansion: 5 Sz-2 H(z)= Sz-2 5-12-¹ 1 4 -5+ ´(z−2)(z+±)¯ (1−2z¯¹)(1+½z¯`¹)¯¯¹−¾z¯'−z² = −5+ -2 1-3z¹. 1-2z a) If the system is causal, then h[n] = −58[n]+2″u[n]+4·½" u[n]. b) If the system is stable, then h[n] = −58[n]−2"u[−n−1]+4·½″ u[n]. = -1 -N