1) A discrete-time, causal and LTI system is shown below. x[n] and y[n] are input and output signals of the system. An) -yin - 1)+tn-2] = a[n] a) Find the system function, H(z), and the impulse response, h[n]. b) Find the step function, s[n], of the system. (Hint: if x[n]=u[n], y[n]=s[n]) c) Find the z-transforms of the signals x[n] = n u[n- 2] and x[n]= u[n – 1]. 4[n] using the properties of the z-transform. Write the results as the functions of X(z). d (Hint: nx[n]<→-z–X(z)) dz

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1) A discrete-time, causal and LTI system is shown below. x[n] and y[n] are input and output signals of
the system.
An) -yin - 1) +tn-2] = a[n]
a) Find the system function, H(z), and the impulse response, h[n].
b) Find the step function, s[n], of the system. (Hint: if x[n]=u[n], y[n]=s[n])
c) Find the z-transforms of the signals x[n] = n u[n- 2] and x[n] =
H u[n- 1 .
4[n]
%3D
using the properties of the z-transform. Write the results as the functions of X(z).
d
(Hint: nx[n]<→-z–X(z))
dz
Transcribed Image Text:1) A discrete-time, causal and LTI system is shown below. x[n] and y[n] are input and output signals of the system. An) -yin - 1) +tn-2] = a[n] a) Find the system function, H(z), and the impulse response, h[n]. b) Find the step function, s[n], of the system. (Hint: if x[n]=u[n], y[n]=s[n]) c) Find the z-transforms of the signals x[n] = n u[n- 2] and x[n] = H u[n- 1 . 4[n] %3D using the properties of the z-transform. Write the results as the functions of X(z). d (Hint: nx[n]<→-z–X(z)) dz
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