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

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b1 Digital signal rpocessıng question.

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
y[n] -y[n - 1] +y[n – 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])
c) Find the z-transforms of the signals x[n] = n u[n-2] and xn]=
u[n – 1].
u[n]
using the properties of the z-transform. Write the results as the functions of X(z).
d
(Hint: nx[n]+>-z X(2))
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 y[n] -y[n - 1] +y[n – 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]) c) Find the z-transforms of the signals x[n] = n u[n-2] and xn]= u[n – 1]. u[n] using the properties of the z-transform. Write the results as the functions of X(z). d (Hint: nx[n]+>-z X(2))
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