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.

A system has fourteen poles and two zeroes. Its high frequency asymptote, in its magnitude plot, has having a slope of

The popular plot of G(s)=$${{10} \over {s{{\left( {s + 1} \right)}^2}}},$$ intercepts real axix at $$\omega = {\omega _0}$$ Then, the real part and $${\omega _0}$$ are respectively given by