Question

Which of the following filters is NOT causal: a) H(Z) = b) H(Z) = 22 Z (z–0.5)(z-2) 23 d) H(2) = (2-0.5)(2-2) c) H(Z) = (2-0.5)(2-2) e) H(Z) = (2+0.5)(2+2) g) H(2) = z[2-0.5)(2-2) z2 22(2-0.5) (2-2) Z 23 h) H(Z) = (2-1)(z-0.5)(2-2)

Answer 1

Important poins : A discrete time LII system with rational transfer function HCK) is causal if and only if ca) The Roc is the exterior of a circle outside the outermost pole. i.ee ROC POTPI (b) With H(Z) expressed as a ratio of polynomialis in Z, the order of the numerator cannot be greater than the order of the denominator * In our problem you didn't mention the Roc. so we go through the second method. Note : Order defination : Highest power of z-term

Z- 1 ca) nica) Numer ator order (NO) = 1 Denominator order ( D.O) - 1 NO DO ... Non Causal system A(Z) = t = 'Iz (b) = z a zl. - 1 I-7 K N.O=0 D.D = 1 DO N.o causal system Z (C) H(#) = - (4-0.5)(2-2) 2² 0.52 + 1 Nộp : 4 D.0 = 2 D. D. > Ny0, causal system

HW - Z (7-5)(2-2) (Z - 252 +1) D.O. - 2 NO = D.O Non Causal System le) (2) 7 7 (2-0.5)(2-2) (72.5% +1) No = 3 DO = 2 N.o > D.D Non causal system If H) 2 74 * (7-0.5)(x-2) (z² 2.5%+ 1) r: 0 - 0 ) D-b : 2 | 0 0 > A. 0, Causal system

19) H(E). (4-0.5)(-2) (7- 2.5% + 1) N.0: 2 ; D.0-2 NO = D.O. i. Non causal system Hlz) = Z (2-1) C2-0.5) (2-2) No - 1 D.O = 3 2.0 > N 0 . Causal system