A sequence x(n) with the z-transform X(z) = z⁴ + z² - 2z + 2 - 3z^-4 is applied as an input to a linear, time-invariant system with the impulse response h(n) = 2δ(n - 3) where
$$\delta \left( n \right) = \left\{ {\matrix{ {1,} & {n = 0} \cr {0,} & {{\rm{otherwise}}} \cr } } \right.$$
The output at n = 4 is

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