Q6.- Consider the LTI system represented by the system function 3 = (1 - - -...

 

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Q6.- Consider the LTI system represented by the system function 3 = (1 - - - -¯-¹) (₁ + ² / -~-¹) (1 - 3= ¯¹). 7 Z 3z 2 H(z) This system function can be factored as H(z) = Hmin (2)· Hap(2), where Hmin(z) is a minimum-phase system and Hap(z) is an allpass system. (a) Sketch the pole-zero plot of this system function. You do not need to indicate the region of convergence. You must indicate any multiple order zeros or poles appropriately. [2 pts] (b) Sketch the pole-zero plots for Hmin(z) and Hap(2). Again, you do not need to indicate the region of convergence, but you must indicate all multiple order poles and zeros. (eja) (c) Give the expressions for Hmin(2) and Hap(z). Show that H ap = 1 for all o as [3 pts] Q6.- Consider the LTI system represented by the system function 3 = (1 - - - -¯-¹) (₁ + ² / -~-¹) (1 - 3= ¯¹). 7 Z 3z 2 H(z) This system function can be factored as H(z) = Hmin (2)· Hap(2), where Hmin(z) is a minimum-phase system and Hap(z) is an allpass system. (a) Sketch the pole-zero plot of this system function. You do not need to indicate the region of convergence. You must indicate any multiple order zeros or poles appropriately. [2 pts] (b) Sketch the pole-zero plots for Hmin(z) and Hap(2). Again, you do not need to indicate the region of convergence, but you must indicate all multiple order poles and zeros. (eja) (c) Give the expressions for Hmin(2) and Hap(z). Show that H ap = 1 for all o as [3 pts]

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