Sketch the pole-zero diagram of the system

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Reference no: EM133146890

Question 1: Determine the z-transform of the following signals and determine the ROC.

a. x(n) = 1/2ⁿu(n - 3) + (0.9)^n-3u(n)
b. y(n) = cos(an)/n.u(n)

Question 2. Determine the causal signal x(n) if its z-transform X(z) is given by:

X(z) = z(z - e^-βcosβ)/z²(z - 2ze^-βcosβ + e^-2β)

Question 3. Given the block diagram of the system below
a. Determine the impulse response, assume a causal system.
b. Is the system stable? Why? Why not?

745_Impulse response.jpg

Question 4. Given the response of an LTI system to an input x(n) = 1/2ⁿ u(n) is the output {0,0,1}= (δ(n - 2). Compute the response of the system y(n) to the input 2cos (Π/3n), that is determine the response y(n). Compute the impulse response h(n).

Question 5. The LTI system is described by the block diagram given
a. Determine the Input / Output equation
b. Determine the system function H(z).
c. Sketch the pole-zero diagram of the system.

895_Impulse response1.jpg

Reference no: EM133146890

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