The Fourier series expansion of a real periodic signal with fundamental frequency f₀ is given by
$${g_p}\left( t \right) = \sum\limits_{n = - \infty }^\infty {{c_n}{e^{j2\pi {f_0}t}}} ;$$
it is given that c₃ = 3 + j5. Then c₃ 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