In this problem you are to design a simple causal real discrete time LTI system

# In this problem you are to design a simple causal

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1.10.4 In this problem you are to design a simple causal real discrete-time LTI system with the following properties:(a) The system should kill the signals (-1)nand cos(0.5n)(b) The system should have unity dc gain. That is,Hf(0) = 1.For the system you design:(a) Find the dierence equation to implement the system.(b) Sketch the impulse response of the system.(c) Roughly sketch the frequency response magnitude|Hf(!)|. Clearly show the nulls of the frequency response.1.10.4) Solution 186 π 0.5 π 0 0.5 π π 0 5 10 15 FREQUENCY RESPONSE 2 ω π 0.5 π 0 0.5 π π 0 2 4 6 8 FREQUENCY RESPONSE 4 ω π 0.5 π 0 0.5 π π 0 2 4 6 8 FREQUENCY RESPONSE 3 ω π 0.5 π 0 0.5 π π 0 2 4 6 FREQUENCY RESPONSE 1 ω 1 0.5 0 0.5 1 1 0.5 0 0.5 1 2 ZERO POLE DIAGRAM 3 1 0.5 0 0.5 1 1 0.5 0 0.5 1 2 ZERO POLE DIAGRAM 1 1 0.5 0 0.5 1 1 0.5 0 0.5 1 ZERO POLE DIAGRAM 2 1 0.5 0 0.5 1 1 0.5 0 0.5 1 ZERO POLE DIAGRAM 4 1.11.1) Solution IMPULSE RESPONSE FREQUENCY RESPONSE POLE-ZERO DIAGRAM 1 2 3 2 4 1 3 3 2 4 1 4 190 1.12.4 Feedback LoopConsider the following connection of two discrete-time LTI systems.--h2(n)-h1(n)6+iYou are told thath1(n) =δ(n) +δ(n-1),h2(n) =12δ(n-1).(a) Find the impulse responseh(n) of the total system.(b) Sketchh1(n),h2(n), andh(n).(c) Find the dierence equation describing the total system.1.12.4) 0 10 20 0.5 0 0.5 1 1.5 2 h 1 (n) [IMPULSE RESPONSE] n 0 10 20 0.5 0 0.5 1 1.5 2 h 2  #### You've reached the end of your free preview.

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