Question

Use the Z-transform to find the general solution (zero-input and zero-state) for the following linear recursive difference equation written in advanced form: y[n+2] +3y[n+1]+2y[n] = 2x[n+2] A. Use the Z-transform to find the zero-input solution with initial conditions: y[-2]=2, and y(-1)=3 B. Use the Z-transform to find the zero-state solution if the source function is given by, x[n]=3" u[n] C. Write the general solution to the linear recursive difference equation D. Use the Z-transform to find the transfer function (H(z)) and the impulse response, h[n] E. Draw the canonical form of the system realization for this system

Answer 1

given diferente equatias ġ in advanced form converting it to delayed foom by shifting whole equahm 2 months gın) +34(n-1) +2y (n-2) - 2011) YIN-1) A Z-ly(2) + Y61) yon-2) 6729€)+9H)2 +91-2) z-transform of above egun Y+3[Z-'Y(2) + YE1] +2[zZyeI+YA+2+yəm = 2 X(2) Y@7 (+32 4+22-23+9+62+'+4= 2XZ) solution, X(2)=0 for zero-input ... YEDE -13-67-/ 1t3Z-'+22-2 -13-62~ YE)= 142:1 (1+22-1) A (1+z + B (1+2z-)) Y(21= )

Å= -13-67 [i+22+1)/ -7-4 27 B = -13-6z- 20 -13+3 = 6) yen lehet a huin) solution Zeio-input 9, cn) = 7 (Hyun) -40 (2)?qin) . @ Zw-state solution, YEI=Y1-2)=0 for zew-state solution *(nl=3 huin)=(num X(22= *z-1 Ven (14 32" te ale 4 21- ( 17) (1720)(1+22-1)

We a de Gree) Less he do - cryonzel, this 같 - 382 | - - cret) NL | c (0) - | Mel ( ) 2 아는 Sun) Comot(ary Zero-state solution

solution general yin)= 42<p (1) +Üz_5() to 3 "um +ful”um – 116 625"um) H ELP Yes , when inital condition gin= © Qл ло. Y(z) [1732' +82-2) = 2 X2)

HZ)= YZ) X(Z) it3z1+22-2 HEI= 2 (+z-)(1+271) 4487= 042-t) *(1+221) VA +27-) As Bal B *** H(ZI= -2 t 4 . Itzal It and It2z1 hen) = -2 E1)"uin) +, 462)" uins 1

0 canonical form of the system realization 2 Hizle Hele hele +27-2 H32 >yini am a