Table of Contents
Is the function periodic if so what is the period?
Definition. Geometrically, a periodic function can be defined as a function whose graph exhibits translational symmetry, i.e. a function f is periodic with period P if the graph of f is invariant under translation in the x -direction by a distance of P .
Is FX 0 a periodic?
Yes, a constant function is periodic with , fundamental period=0 as it is the smallest positive value for the period.
Is a constant function a periodic function?
P is the period of the function. A constant function, f(x)=c repeats its values at regular intervals.
How do you know if a signal is periodic or not?
In mathematical terms a signal x(t) is periodic if there is a number T such that for all t Equation 10.10 holds. The smallest positive number T that satisfies Equation 10.10 is the period and it defines the duration of one complete cycle.
What is periodic and non-periodic function?
The basic definition for a periodic function looks fairly straightforward: it repeats its values at set intervals, called periods. This common definition might lead you to think that non-periodic functions are simply those that don’t repeat at set intervals.
How to prove a function is periodic with no fundamental period?
If f (x) is a function with period P, then f (ax), where ‘a’ is non – zero real number, is periodic with period P/|a| = 2π/|a| d) If a constant is added, subtracted, multiplied, or divided in the periodic function, period remains the same. e) Every constant function is always periodic, with no fundamental period.
When is g(f(x)) periodic with period T?
If f (x) is a periodic function with period T and g (x) is any function such that range of ‘f’ is a proper subset of the domain of g, then g (f (x)) is periodic with period T. We were unable to load Disqus.
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.
How do you find the periodicity of a function?
A function f is said to be periodic if, for some non-zero constant P, it is the case that: f (x+P) = f (x) For all values of x in the domain. A non-zero constant P for which this is the case is called a period of the function.