Consider the circuit given in fig. using an ideal operational Amplifier.

The characteristics of the diode are given by the relation I = I_s $$\left[ {{e^{{{qV} \over {KT}}}} - 1} \right],$$

Where V is the forward voltage across the diode
(a)Express V₀ as a function of V_i assuming V_i> 0.
(b)If R = 100K$$\Omega $$ , I_s = 1$$\mu $$A and $${{KT} \over q}\,\, = \,\,25mV$$

The line code that has zero dc component for pulse transmission of random binary data is

A deterministic signal has the power spectrum given in figure. The minimum sampling rate needed to completely represent this signal is

A probability density function is given by $$p(x) = \,K\,\,\exp \,\,( - \,{x^2}/2),\,\, - \,\infty \, < \,x < \,\infty $$.

The value of K should be