The DTFT of a sequence $x\left[ n \right]$ is given by $X\left( {{e^{iω }}} \right)$. Since $X\left( {{e^{iω }}} \right)$ is period function of ω, it can be expressed classical Fourier series as,$X\left( {{e^{iω }}} \right) = \sum\limits_{n = - \infty }^\infty {{C_n}{e^{in{ω _0}ω }}} $Where ω0 is a fundamental frequency. Which of the following statement is correct?

Question

The DTFT of a sequence $x\left[ n \right]$ is given by $X\left( {{e^{iω }}} \right)$. Since $X\left( {{e^{iω }}} \right)$ is period function of ω, it can be expressed classical Fourier series as,$X\left( {{e^{iω }}} \right) = \sum\limits_{n = - \infty }^\infty {{C_n}{e^{in{ω _0}ω }}} $Where ω0 is a fundamental frequency. Which of the following statement is correct?

TuteeHUB · Accepted Answer

ω0 = 1, ${C_n} = - x\left[ -n \right]$

TuteeHUB · Answer

${\omega _0} = \pi$, ${C_n} = - x\left[ n \right]$

TuteeHUB · Answer

${\omega _0} = \pi$, ${C_n} = x\left[ -n \right]$

TuteeHUB · Answer

ω0 = 1, ${C_n} = x\left[ -n \right]$

1.	The DTFT of a sequence \(x\left[ n \right]\) is given by \(X\left( {{e^{iω }}} \right)\). Since \(X\left( {{e^{iω }}} \right)\) is period function of ω, it can be expressed classical Fourier series as,\(X\left( {{e^{iω }}} \right) = \sum\limits_{n = - \infty }^\infty {{C_n}{e^{in{ω _0}ω }}} \)Where ω0 is a fundamental frequency. Which of the following statement is correct?
A.	\({\omega _0} = \pi\), \({C_n} = - x\left[ n \right]\)
B.	\({\omega _0} = \pi\), \({C_n} = x\left[ -n \right]\)
C.	ω0 = 1, \({C_n} = x\left[ -n \right]\)
D.	ω0 = 1, \({C_n} = - x\left[ -n \right]\)
Answer» D. ω0 = 1, \({C_n} = - x\left[ -n \right]\)

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