Sum of periodic signals

1. Is the sum of periodic signals periodic?
2. Is the sum of two periodic signals periodic?
3. How do you calculate periodic signals?
4. Is the sum of discrete time periodic signals periodic?

Is the sum of periodic signals periodic?

Sums of periodic functions are not always periodic

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

Is the sum of two periodic signals periodic?

The sum of two periodic signals is generally periodic if the two signals have the same period. If the periods of the two signals are different, the sum may or may not be periodic depending on the relationship between the periods.

How do you calculate periodic signals?

Periodic Functions

x(t) = x(t + nT). The minimum value of T that satisfies x(t) = x(t + T) is called the fundamental period of the signal and we denote it as T₀. Examples of periodic signals are infinite sine and cosine waves. Examples: Given x₁(t) = cos(3t), and x₂(t) = sin(5t).

Is the sum of discrete time periodic signals periodic?

Abstract—Unlike the continuous case, given two discrete pe- riodic signals, their sum is always periodic. We give a char- acterization 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.