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Seminar-12-Z-Transform-I

Seminar-12-Z-Transform-I - Senyals i Sistemes ESUP UPF...

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Senyals i Sistemes ESUP, UPF Seminar 12: Z-Transform (part I) 1. Calculate the z-transform for the following signals (a) x 1 [ n ]=[ n ] (b) x 2 [ n ]=[ n 7 ] (c) x 3 [ n ]= 2 [ n ]− 3 [ n 1 ] 4 [ n 3 ] 2. You are given the z-transform for two signals x 1 [ n ] X 1 z = 3 2z 1 x 2 [ n ] X 2 z = 1 z 2 Use the superposition and time-delay properties of the z-transform to calculate Y z if y [ n ] is given by y [ n ]=− x 1 [ n ] 2x 2 [ n 1 ] 3. Given the z-transform of the following systems, find their impulse response: (a) H 1 z = 2 z 1 3z 3 (b) H 2 z = z z 1 (Note: This system is not causal!) (c) H 3 z = 1 z 2  1 z 2 (d) H 4 z = 1 e j / 3 z 1  1 e j / 3 z 1 (Note: h 4 [ n ] is real.) 4. Suppose an LTI system has a system function H z = 1 5z 1 3z 2 2.5z 3 4z 8 (a) Determine the difference equation that relates the output of the system y [ n ] to

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Seminar-12-Z-Transform-I - Senyals i Sistemes ESUP UPF...

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