EECE 340 Homework, Spring 2008

EECE 340-Signals and Systems Homework #9 Problem #1 The block diagram of a discrete-time system is shown in the figure below. x(n) y(n) —+O) > w(n) - z! L; L2 a) Write the difference equations relating x(7), w()and y(n). b) Find the transfer function, H(z), of the system by applying the Z-transform to the equations determined in Part (a). c) Plot the signal flow graph of the above block diagram. Problem # 2 The block diagram of a discrete-time system is shown in the figure below. x(n) ~p y(n), ry v -0.64 a) Determine the transfer function, H (z), of the system. b) Determine the magnitude frequency responsre, |H(@)|, of the system using the pole-zero plot of H (z). Page 1 of 2 Problem # 3 Consider an LTI discrete-time system with transfer function given by: 1-2cosOz! +z7 H(Z)=—_—— (2) 1-2rcos@z1+r?27 Draw the signal flow graph in direct form (I), direct form (II) and transpose of direct form (II). Problem # 4 Consider the following difference equation: 1 3 1 y(n) = x(n) +x -1) +79 -) ten -2) Draw the signal flow graph of the above difference equation in: a) Direct form I b) Direct form II c) Transpose of direct form I d) Transpose of direct form II Problem #5 Consider an LTI discrete-time system represented by the block diagram shown below. x(n) w(n) y(n) Determine the transfer function, H(z), and the unit sample (impulse) response of the system. Page 2 of 2 ; / EECE 34-0 HenewotR #29 Soliton /7 i ge jar! | a) 7) =r iy+h WCA-~P) Won) = 46) +4 L, w Cn—L) Dz = Xj 4+hzZ'wiey © WE) = YX + L, 2! wl) @ => wwli-l.¢/] =v @ Ii, g@! Hip lave a Dox Ya)[1- 4 2 _] = x02 (L.L, 2° => WW (ey— VOY — !-4. = AOQY 1 CL, +h)! fl = x (n)—? Ap ln - 3) + & Or 2) VY (2) = Le — aE yer 2 Key PN I Ye = = x Ca) )4 F°S ; e*) 207g Kah! 427] Te yz) l-20en -2) Cn x —- ~y C70. (h 2p (nh) — pa (1) = >t |) -- Cyiey) -! te cae Wn