1) A discrete-time, causal and LTI system is shown below. x[n] and y[n] are input and output signals of the system. 3 ln] -ytn-1]+yin- 2] = x[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]) n-1 c) Find the z-transforms of the signals x[n] = n- u[n- 2] and x[n] = u[n] using the properties of the z-transform. Write the results as the functions of X(z). d (Hint: nx[n]<→-:÷X(:)) dz

Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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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.
3
Mn] -n-1]+yn-2]= x[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])
n-1
c) Find the z-transforms of the signals x[n] = n u[n-2] and x[n] =
using the properties of the z-transform. Write the results as the functions of X(z).
d
(Hint: nx[n]<²→-:÷x(:))
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. 3 Mn] -n-1]+yn-2]= x[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]) n-1 c) Find the z-transforms of the signals x[n] = n u[n-2] and x[n] = using the properties of the z-transform. Write the results as the functions of X(z). d (Hint: nx[n]<²→-:÷x(:)) dz
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