Fourier coefficients of two discrete-time signals of different periods

1. How do you add two discrete signals?
2. Is discrete time Fourier series periodic?

How do you add two discrete signals?

In order to simultaneously shift and add two discrete time signals, we can only make use of indices of x1 and x2 which can only be positive integers. So, for y[n] = x1[n-2]+x2[n], n should always be greater than 3.

Is discrete time Fourier series periodic?

In digital signal processing, the term Discrete Fourier series (DFS) is any periodic discrete-time signal comprising harmonically-related (i.e. Fourier) discrete real sinusoids or discrete complex exponentials, combined by a weighted summation.