The discrete Fourier series representation for the following sequence:
\(x\left( n \right) = \cos \frac{\pi }{4}n\) is1
\(\frac{1}{2}{e^{j{{\rm{\Omega }}_0}n}} + \frac{1}{2}{e^{ - j{{\rm{\Omega }}_0}n}}\) and \({{\rm{\Omega }}_0} = \frac{\pi }{8}\)
2
\(\frac{1}{2}{e^{ - j{{\rm{\Omega }}_0}n}} + \frac{1}{2}{e^{ - j2{{\rm{\Omega }}_0}n}}\) and \({{\rm{\Omega }}_0} = \frac{\pi }{4}\)
3
\(\frac{1}{2}{e^{ - j{{\rm{\Omega }}_0}n}} + \frac{1}{2}{e^{ - j{{\rm{\Omega }}_0}n}}\) and \({{\rm{\Omega }}_0} = \frac{\pi }{6}\)
4
\(\frac{1}{2}{e^{j{{\rm{\Omega }}_0}n}} + \frac{1}{2}{e^{j7{{\rm{\Omega }}_0}n}}\) and \({{\rm{\Omega }}_0} = \frac{\pi }{4}\)