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...

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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<br>the system.<br>3<br>y[n] -y[n - 1] +y[n – 2] = x[n]<br>a) Find the system function, H(z), and the impulse response, h[n].<br>b) Find the step function, s[n], of the system. (Hint: if x[n]=u[n], y[n]=s[n])<br>c) Find the z-transforms of the signals x[n] = n u[n-2] and xn]=<br>u[n – 1].<br>u[n]<br>using the properties of the z-transform. Write the results as the functions of X(z).<br>d<br>(Hint: nx[n]+>-z X(2))<br>

Extracted 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))

Jun 11, 2022

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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 y[n] -y[n - 1] +y[n – 2] = x[n] a) Find the system function, H(z), and the impulse...

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