Is sum of periodic function is 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 two periodic functions a periodic function?

Sums of several periodic functions with the common domain. It is well known that the sum of two continuous periodic functions on R is periodic if and only if their periods are commensurable. are bounded and periodic, their periods are incommensurable, but the sum f1 + f2 is periodic.

Can the sum of 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.

How do you know if a function is periodic?

1. A function f(x) is said to be periodic, if there exists a positive real number T such that f(x+T) = f(x).
2. The smallest value of T is called the period of the function.
3. Note: If the value of T is independent of x then f(x) is periodic, and if T is dependent, then f(x) is non-periodic.

How do you know if a function is periodic or not?

In order to determine periodicity and period of a function, we can follow the algorithm as :

• Put f(x+T) = f(x).
• If there exists a positive number “T” satisfying equation in “1” and it is independent of “x”, then f(x) is periodic.
• The least value of “T” is the period of the periodic function.

How do you know if a function is not periodic?

In order to determine periodicity and period of a function, we can follow the algorithm as :

1. Put f(x+T) = f(x).
2. If there exists a positive number “T” satisfying equation in “1” and it is independent of “x”, then f(x) is periodic.
3. The least value of “T” is the period of the periodic function.

How do you know if a sequence is periodic?

A sequence is called periodic if it repeats itself over and over again at regular intervals. Formally, a sequence u1, u2, … is periodic with period T (where T>0) if un+T=un for all n≥1. The smallest such T is called the least period (or often just “the period”) of the sequence.

What is the order of a periodic sequence?

If you’re reading the hours on the clock, it goes in the following sequence: 1,2,3,4,5,6,7,8,9,10,11,12,1,2,…. Because this repeats forever, we know the sequence of hours on a clock is periodic!

Why doesn’t the sum of two periodic functions have an LCM?

The reason is that the two functions have periods that are not rational multiples of each other. The period of the sum of periodic functions is the least common multiple of the periods of all the functions, but when they are not rational multiples of each other, it doesn’t make sense to talk about the LCM of them.

How do you prove that a function is periodic?

If and are two periodic functions with periods and respectively, then if the ratio is rational, then for any function , the function is also periodic. And you also know that this fails when the ratio is not rational.

How to find the period of combination of two functions?

Many a times it is asked to find the period of combination of two functions given the period of individual functions. x is π but how to find the period of f ( x)? If f ( x) and g ( x) are periodic functions with period 7 and 11 respectively. Then the period of F ( x) = f ( x) g ( x / 5) − g ( x) f ( x / 3)

Why doesn’t this graph look periodic?

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.