# HW8_S - HW 8 ECE 3704 Due 21.6.3(5(a Find the transfer...

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DKL:5/6/10 HW 8 1/8 HW 8 ECE 3704 Due 5-4-10 21.6.3 (5) (a) Find the transfer function of the system shown in Figure P21.6.3 by block diagram reduction. (b) (5) Write the difference equations for this system in delay form. (c) (5) Draw the pole zero diagram. Figure P21.6.3 Solution This problem illustrates the relationship between block diagrams, transfer functions, and difference equations.

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DKL:5/6/10 HW 8 2/8 The overall transfer function is just the cascade of these two subsystems. We have Y ( z ) X ( z ) = 1 + 2.41 z 1 + 2.41 z 2 + z 3 1 + 0.81 z 2 (b) From the transfer function we obtain 1 + 0.81 z 2 ( ) Y ( z ) = 1 + 2.41 z 1 + 2.41 z 2 + z 3 ( ) X ( z ) So we obtain the difference equation y ( n ) + 0.81 y ( n 2) = x ( n ) + 2.41 x ( n 1) + 2.41 x ( n 2) + x ( n 3) (c) To compute poles and zeros Y ( z ) X ( z ) = 1 + 2.41 z 1 + 2.41 z 2 + z 3 1 + 0.81 z 2 z 3 z 3 = z 3 + 2.41 z 2 + 2.41 z + 1 z 3 + 0.81 z
DKL:5/6/10 HW 8 3/8 23.1.3 A simple FIR notch filter is given by Y ( z ) X ( z ) = H ( z ) = 1 2cos( Ω 0 ) z 1 + z 2 (a) (10) Show that the zeros of this transfer function are given by z = e ± j Ω 0 .

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