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)

Let a frequency modulated (FM) signal $$x(t) = A\cos ({\omega _c}t + {k_f}\int_{ - \infty }^t {m(\lambda )d\lambda )} $$, where $$m(t)$$ is a message signal of bandwidth W. It is passed through a non-linear system with output $$y(t) = 2x(t) + 5{(x(t))^2}$$. Let $${B^T}$$ denote the FM bandwidth. The minimum value of $${\omega _c}$$ required to recover $$x(t)$$ from $$y(t)$$ is