Question

find the unit impulse response of

y(k) - 0.6y(k-1) - 0.16y(k-2) = 5f(k) ?

Answer 1

Givent Y(&)-0.67Ck.-1) -0.16 y(K-2) = 5fCk) the unit impulse response of the system (H(z)) : lieu isput FCk)=8(k) - Lunit impulse . 84)-06 86 –) -0-14 % ) : 550k) . applying 2-toans fami- ^(7) ~087'YZ) -0.18 7-24(7)587) Y(7)[1-0-67-1-0-16 -1) = 5 8C7) .. H(a) = como elemente

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After doing factorization to the denominator , H(7) = - .. Citazz-1) (1747-1) HCZ) = 5 C--) (1+z) Applying partial fractions, Hz): À + B (-12-"). (1+=) Aften solving above coefficients, we get A = 4, B=2 HCZ) = 4 + 1 - 1 4 3 2 1 1ttz! poles are at z = 4/3 & -/s → case :- h[n] is right sided ROC: 171 > 1451 Rogion of convergence. D as bing4) " urny +36-5)Yuring ROC

care- l hing is left sided ROC ROC: 1714 15l fumate b[n] = 4 C)" (-uf-n-1) +16+)(uf-n-I) Case ir hrn] is two sided ROC: 1}}<z«141 hangaa (9)Pucn] +16+) C-uf-n-) img TIDAROC ft 941 Real

Givent Y(&)-0.67Ck.-1) -0.16 y(K-2) = 5fCk) the unit impulse response of the system (H(z)) : lieu isput FCk)=8(k) - Lunit impulse . 84)-06 86 –) -0-14 % ) : 550k) . applying 2-toans fami- ^(7) ~087'YZ) -0.18 7-24(7)587) Y(7)[1-0-67-1-0-16 -1) = 5 8C7) .. H(a) = como elemente