White Gaussian noise is passed through a linear narrow band filter. The probability density function of the envelope of the noise at the filter output is:

The variance of a random variable X is $$\sigma _x^2\,.$$ Then the variance of - kx (where k is a positive constant ) is

A rectangular pulse existing between t = 0 and t = T and having an amplitude A is to be received by a matched filter

(a) Draw the impulse response of the matched filter labeling all important points and the axes.
(b) Find the signal shape at the filter output. Lable all important points and axes.

A system with derivative control is shown in figure.
(a)Determine the transfer function and the characteristic equation of the system.

(b)Given that K > 0, find the range of '$$\tau $$' for which the system is unconditionally stable.