The z-transform X[z] of a sequence x[n] is given by $$X\left[ z \right] = {{0.5} \over {1 - 2{z^{ - 1}}}}.$$    It is given that the region of convergence of X[z] includes the unit circle. The value of x[0] is

The Fourier transform of a real valued time signal has

A. Odd symmetry

B. Even symmetry

C. Conjugate symmetry

D. No symmetry

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. $$V$$

B. $${{{T_1} - {T_2}} \over T}V$$

C. $${V \over {\sqrt 2 }}$$

D. $${{{T_1}} \over {{T_2}}}V$$

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?

A. $$T = \sqrt 2 {T_s}$$

B. T = 1.2T_s

C. Always

D. Never

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

A. $${{\alpha - \beta } \over {\alpha + \beta }}$$

B. $${{\alpha \beta } \over {\alpha + \beta }}$$

C. α

D. β