A continuous time LTI system is described by $$\frac{{{d^2}y\left( t \right)}}{{d{t^2}}} + 4\frac{{dy\left( t \right)}}{{dt}} + 3y\left( t \right) = 2\frac{{dx\left( t \right)}}{{dt}} + 4x\left( t \right)$$
Assuming zero initial conditions, the response y(t) of the above system for the input x(t) = e^-2tu(t) is given by

The Fourier transform of a real valued time signal has

The RMS value of a rectangular wave of period T, having a value of +V for a duration, T₁(< T) and -V for the duration, T - T₁ = T₂ equals

A continuous time function x(t) is periodic with period T. The function is sampled uniformly with a sampling period T_s. In which one of the following cases is the sampled signal periodic?

The phase response of a passband waveform at the receiver is given by
$$\varphi \left( f \right) = - 2\pi \alpha \left( {f - {f_c}} \right) - 2\alpha \beta {f_c},$$
where f_c is the centre frequency, and α and β are positive constants. The actual signal propagation delay from the transmittance to receiver is