The discrete-time Fourier series representation of a signal x[n] with period N is written as $\mathrm{x}[\mathrm{n}]=\sum _{\mathrm{k}=0}^{\mathrm{N}-1}{\mathrm{a}}_{\mathrm{k}}{\mathrm{e}}^{\mathrm{j}(2\mathrm{k}\mathrm{n}\pi /\mathrm{N})}$. A discrete-time periodic signal with period N = 3, has the non-zero Fourier series coefficients: a_-3 = 2 and a₄ = 1. The signal is

Options :

1. $2+2{\mathrm{e}}^{-\left(\mathrm{j}\frac{2\pi }{6}\mathrm{n}\right)}\cos \left(\frac{2\pi }{6}\mathrm{n}\right)$

2. $1+2{\mathrm{e}}^{\left(\mathrm{j}\frac{2\pi }{3}\mathrm{n}\right)}\cos \left(\frac{2\pi }{6}\mathrm{n}\right)$

3. $1+2{\mathrm{e}}^{\left(\mathrm{j}\frac{2\pi }{6}\mathrm{n}\right)}\cos \left(\frac{2\pi }{6}\mathrm{n}\right)$

4. $2+2{\mathrm{e}}^{\left(\mathrm{j}\frac{2\pi }{6}\mathrm{n}\right)}\cos \left(\frac{2\pi }{6}\mathrm{n}\right)$