Is the constant function periodic if so what is its period?

The constant function f ( x ) = c , where c is independent of x, is periodic with any period, but lacks a fundamental period.

Is a constant a periodic signal?

As you say, the constant function is periodic. So, a constant signal is periodic, it has an uncountably infinite number of periods (since any real number p>0 is a period), but it does not have a fundamental period.

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

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.

Can a function have no period?

‘ you’ll have to give this answer: Sorry—constant functions don’t have a least positive period. There are also non-constant periodic functions with no least positive period. For example, define a function f to be 1 for rational inputs, and 0 for irrational inputs.

What is a constant signal?

A constant signal has zero frequency, while a signal that changes very fast over time has high frequencies. Clearly, the higher the frequencies in a signal, the more samples would be needed to represent it with no loss of information thus requiring that Ts be small.

What is not a periodic function?

A non-periodic function does not remain self-similar for all integer multiples of its period. A decaying exponential is an example of a non-periodic function. The distance between consecutive peaks does not remain constant for all values of $ x $, nor does the amplitude of consecutive peaks remain constant.

Which of the following function is not periodic?

So cos(x2) is not periodic.

When is a function constant?

In mathematics, a constant function is a function whose (output) value is the same for every input value. For example, the function y(x) = 4 is a constant function because the value of y(x) is 4 regardless of the input value x (see image).

Which one is a constant function?

A constant function is a function which takes the same value for f(x) no matter what x is. When we are talking about a generic constant function, we usually write f(x) = c, where c is some unspecified constant. Examples of constant functions include f(x) = 0, f(x) = 1, f(x) = π, f(x) = −0.

What is a period in a periodic function?

The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function. In other words, a periodic function is a function that repeats its values after every particular interval.

Can a constant function be a periodic function?

There is nothing in the definition of periodic function that says that is not allowed. Yes, a constant function is a periodic function with any T∈R as its period (as f (x)=f (x+ T) always for howsoever small ‘T’ you can find). However, the fundamental period of a constant function is not defined for the above reason.

What is the fundamental period of a constant?

Answer to your question: Constants are periodic functions of any period and, therefore, they do not have a fundamental period. Nowhere in the definition of a period function is it stated that the function must have a least period. If f(x) = c then for any p we have f(x + p) = f(x).

What is the difference between periodic and periodic function?

Period of a Function The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function. In other words, a periodic function is a function that repeats its values after every particular interval.

What is the least period of a period function?

Nowhere in the definition of a period function is it stated that the function must have a least period. If f ( x) = c then for any p we have f ( x + p) = f ( x). So f is periodic and p is a period. Obviously any other non-negative value will also be a period. There is nothing in the definition of periodic function that says that is not allowed.