Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part47

Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part47

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Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition 9 29 Copyright © Orchard Publications The Inverse Z Transform 12*z/(z+1)/(z-1)^2 We can also use the MATLAB dimpulse function to compute and display for any range of values of . The following script will display the first 20 values of in (9.82). % First, we must express the denominator of F(z) as a polynomial denpol=collect((z+1)*((z 1)^2)) denpol = z^3-z^2-z+1 num=[12 0]; % The coefficients of the numerator of F(z) in (9.81) den=[1 1 1 1]; % The coefficients of the denominator in polynomial form fn=dimpulse(num,den,20) % Compute the first 20 values of f[n] fn = 0 0 12 12 24 24 36 36 48 48 60 60 72 72 84 84 96 96 108 108 The MATLAB function dimpulse(num,den) plots the impulse response of the polynomial transfer function where and contain the polynomial coefficients in descending powers of . Thus, the MATLAB script num=[0 0 12 0]; den=[1 1 1 1]; dimpulse(num,den) displays the plot of Figure 9.7. fn [] nf n Gz () num z den z = z
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Chapter 9 Discrete Time Systems and the Z Transform 9 30 Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition Copyright © Orchard Publications Figure 9.7. The impulse response for Example 9.5 Example 9.6 Use the partial fraction expansion method to compute the Inverse Z transform of (9.83) Solution: Dividing both sides by and performing partial fraction expansion, we obtain (9.84) The residues are Then, or Fz () z1 + z 2 2z 2 ++ ------------------------------------------------ = z z ---------- + zz 1 z 2 2 --------------------------------------------------- r 1 z --- r 2 ----------- r 3 j + ------------------------ r 4 z1j + == r 1 + z 2 2 z0 = 1 2 ----- 0 . 5 = r 2 + z z 2 2 --------------------------------------- = 2 5 -- 0 . 4 = r 3 + z ------------------------------------------------- j + = j 1 j + 2 j + j2 -------------------------------------------------- 0 . 0 5 j 0 . 1 5 + = r 4 r 3 0.05 j0.15 z + z 2 2 0.5 z 0.4 0.05 j0.15 + + ---------------------------- 0.05 j0.15 +
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Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition 9 31 Copyright © Orchard Publications The Inverse Z Transform Recalling that and for , we find that the discrete time sequence is or (9.85) We will use the MATLAB dimpulse function to display the first 8 values of in (9.85). We recall that his function requires that
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This note was uploaded on 11/20/2009 for the course EE EE 102 taught by Professor Bar during the Fall '09 term at UCLA.

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Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part47

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