Sum of periodic functions

1. Is the sum of 2 periodic functions always periodic?
2. Is the sum of periodic functions always periodic?
3. Can the sum of a periodic function and a non periodic function be periodic?

Is the sum of 2 periodic functions always periodic?

Unlike the continuous case, given two discrete periodic signals, their sum is always periodic. We give a characterization for the period of the sum; as shown, the least common multiple of the periods of the signals being added is not necessarily the period of the sum.

Is the sum of periodic functions always periodic?

Sums of periodic functions are not always periodic

, whose terms have least periods 2π and 2 respectively.

Can the sum of a periodic function and a non periodic function be periodic?

Let f(x)=x−[x] and g(x)=tanx. This will show that the sum of two periodic functions need not be a periodic function. ...