Sum of two periodic signals

D. Explanation: sum of two periodic signals is a periodic signal only when the ratio of their time periods is a rational number or it is the ratio of two integers. for e.g., t1/t2 = 5/7 → periodic; t1/t2 = 5 → aperiodic.

1. Is the sum of 2 periodic signals periodic?
2. How do you find the sum of two periodic functions?
3. How do you calculate periodic signals?

Is the sum of 2 periodic signals periodic?

Sums of periodic functions are not always periodic

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

How do you find the sum of two periodic functions?

Periodic functions all have the same form that f(x) = f(x+a). Let's say f(x) = f(x+a) and g(x) = g(x+b). So for functions of the same period (a=b): Sum: f(x) + g(x) = h(x) = f(x+a) + g(x+a) = h(x+a).

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).