A signal $$2\cos \left( {{{2\pi } \over 3}t} \right) - \cos \left( {\pi t} \right)$$     is the input to an LTI system with the transfer function $$H\left( s \right) = {e^s} + {e^{ - s}}$$
If C_k denote the k^th coefficient in the exponential Fourier series of the output signal, then C₃ is equal to

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