Periodic

Sum of periodic functions

Sum of periodic functions
  1. What is sum of two periodic functions?
  2. Is the sum of two periodic functions still periodic?
  3. Can sum of a periodic and non periodic function be periodic?

What is sum of two periodic functions?

The identity function is the sum of two periodic functions

Choose two distinct elements . Then . Let and . Then has period d, has period c, and.

Is the sum of two periodic functions still periodic?

Answer: Not necessarily. It doesn't look periodic because it isn't. The reason is that the two functions have periods that are not rational multiples of each other.

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

Yes, it is possible. For example, , satisfy the property. is clearly periodic, and the sum, which is is also periodic.

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