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?
1
\({\omega _0} = \pi\), \({C_n} = - x\left[ n \right]\)
2
\({\omega _0} = \pi\), \({C_n} = x\left[ -n \right]\)
3
ω0 = 1, \({C_n} = x\left[ -n \right]\)
4
ω0 = 1, \({C_n} = - x\left[ -n \right]\)