Let X[k] = k + 1, 0 ≤ k ≤ 7 be 8-point DFT of a sequence x[n],

where X[k] = $$\sum\limits_{n = 0}^{N - 1} {x\left[ n \right]{e^{ - j2\pi nk/N}}} $$.

The value (correct to two decimal places) of $$\sum\limits_{n = 0}^3 {x\left[ {2n} \right]} $$ is ___________.

Let 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this series are denoted by 𝑎_𝑘, that is

$$x\left( t \right) = \sum\limits_{k = - \infty }^\infty {{a_k}} {e^{jk{{2\pi } \over T}t}}$$

The same function 𝑥(𝑡) can also be considered as a periodic function with period T' = 40. Let b_k be the Fourier series coefficients when period is taken as T'. If $$\sum\limits_{k = - \infty }^\infty {\left| {{a_k}} \right|} = 16$$, then $$\sum\limits_{k = - \infty }^\infty {\left| {{b_k}} \right|} = 16$$ is equal to

A discrete time all-pass system has two of its poles at 0.25$$\angle 0^\circ $$ and $$\angle 30^\circ $$. Which one of the following statements about the system is TRUE?

A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height. What is the height of the lamp post in meters?