The magnitude and phase of the complex Fourier series coefficients ${{\rm{a}}_{\rm{K}}}$ of a periodic signal ${\rm{x}}\left( {\rm{t}} \right)$ are shown in the figure. Choose the correct statement form the four choices given. Notation: C is the set of complex numbers, R is the set of purely real numbers, and P is the set purely imaginary numbers.

Question

The magnitude and phase of the complex Fourier series coefficients ${{\rm{a}}_{\rm{K}}}$ of a periodic signal ${\rm{x}}\left( {\rm{t}} \right)$ are shown in the figure. Choose the correct statement form the four choices given. Notation: C is the set of complex numbers, R is the set of purely real numbers, and P is the set purely imaginary numbers.

TuteeHUB · Accepted Answer

${\rm{x}}\left( {\rm{t}} \right) \in {\rm{\;P}}$

TuteeHUB · Answer

${\rm{x}}\left( {\rm{t}} \right) \in {\rm{\;R}}$

TuteeHUB · Answer

${\rm{x}}\left( {\rm{t}} \right) \in {\rm{\;}}\left( {{\rm{C}} - {\rm{R}}} \right)$

TuteeHUB · Answer

The information given is not sufficient to draw any conclusion about x(t)

1.	The magnitude and phase of the complex Fourier series coefficients \({{\rm{a}}_{\rm{K}}}\) of a periodic signal \({\rm{x}}\left( {\rm{t}} \right)\) are shown in the figure. Choose the correct statement form the four choices given. Notation: C is the set of complex numbers, R is the set of purely real numbers, and P is the set purely imaginary numbers.
A.	\({\rm{x}}\left( {\rm{t}} \right) \in {\rm{\;R}}\)
B.	\({\rm{x}}\left( {\rm{t}} \right) \in {\rm{\;P}}\)
C.	\({\rm{x}}\left( {\rm{t}} \right) \in {\rm{\;}}\left( {{\rm{C}} - {\rm{R}}} \right)\)
D.	The information given is not sufficient to draw any conclusion about x(t)
Answer» B. \({\rm{x}}\left( {\rm{t}} \right) \in {\rm{\;P}}\)

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