The DFT of a vector [a b c d] is the vector [α β γ δ]. Consider the product
\[\left[ {p\,q\,r\,s} \right] = \left[ {a\,b\,c\,d} \right]\left[ {\begin{array}{*{20}{c}} a&b&c&d \\ d&a&b&c \\ c&d&a&b \\ b&c&d&a \end{array}} \right]\]
The DFT of the vector [p q r s] is a scaled version of

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