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,...

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>Mn] -n-1]+yn-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>n-1<br>c) Find the z-transforms of the signals x[n] = n u[n-2] and x[n] =<br>using the properties of the z-transform. Write the results as the functions of X(z).<br>d<br>(Hint: nx[n]<²→-:÷x(:))<br>dz<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 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(:))>

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

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