In the circuit shown below, D$$_1$$ and D$$_2$$ are silicon diodes with cut-in voltage of 0.7 V. $$\mathrm{V_{IN}}$$ and $$\mathrm{V_{OUT}}$$ are input and output voltages in volts. The transfer characteristic is

A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of 1 $$\mu$$s. The time for the sampling switch to stay closed to charge a capacitor adequately to a full scale voltage of 1 V with 12-bit accuracy is ___________ $$\mu$$s (rounded off to two decimal places).

For a real signal, which of the following is/are valid power spectral density/densities?

A random variable X, distributed normally as N(0, 1), undergoes the transformation Y = h(X), given in the figure. The form of the probability density function of Y is

(In the options given below, a, b, c are non-zero constants and g(y) is piece-wise continuous function)