A two-port network shown below is excited by external dc sources. The voltages and the currents are measured with voltmeters $${V_1}$$, $${V_2}$$ and ammeter $${A_1}$$, $${A_2}$$ (all assumed to be ideal), as indicated. Under following switch conditions, the readings obtained are:

(i) $${S_1} - open,\,\,\,\,{S_2} - closed$$
$${A_1} = 0\,A,\,\,\,\,\,\,{V_1} = \,4.5\,\,V,$$
$${V_2}\, = \,1.5\,V,\,\,\,\,{A_2}\, = \,1\,A$$

(ii) $${S_1} - Closed,\,\,\,\,{S_2} - Open$$
$${A_1} = 4\,A,\,\,\,\,\,\,{V_1} = \,6\,\,V,$$
$${V_2}\, = \,6\,V,\,\,\,\,{A_2}\, = \,0\,A$$

The z-parameter matrix for this network is

{x(n)} is a real-valued periodic sequence with a period N. x(n) and X(k) form N-point. Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence
y (n) = $${1 \over N}\,\sum\limits_{r = 0}^{N - 1} x \,\left( r \right)x\,(n + r\,)$$ is

In the following network (Fig .1), the switch is closed at t = 0- and the sampling starts from t = 0. The sampling frequency is 10 Hz.
The expression and the region of convergence of the z-transform of the sampled signal are

In the following network (Fig.1), the switch is closed at t = 0 and the sampling starts from t=0. The sampling frequency is 10 Hz.

The samples x (n) (n=0, 1, 2,...........) are given by