In the previous section we have seen that every periodic signal $x(t)$, with Fundamental period $T_0 = 1/F_0$, can be written as a sum of weighted harmonic related phasor components. In theory the summation can contain an infinite amount of components which leads to the following Fourier series expansion:
$$\bbox[5px,border:1px solid black]{ x(t) = \sum_{k=-\infty}^{\infty} \alpha_k e^{j2\pi kF_0 t}.} $$
Thus when the spectral weights, which are represented by the complex numbers $\alpha_k$, are known we can construct (synthesize) the periodic signal $x(t)$ according the above general expression.