Periodicity of a Function: How to Determine if a Function is Periodic

  • Thread starter rafnhy
  • Start date
  • Tags
    Function
In summary, the conversation discusses the periodicity of a function in the discrete domain. It is mentioned that a periodic function must satisfy x[n] = x[n+N], where N is a positive integer and the fundamental period. The issue arises when trying to determine if a function, specifically e^(j3π(n+1/2)/5), is periodic. Attempts were made using the Euler equivalent, but a solution was not found. A photo was also attached, but it was not clear. Based on the discussion, it was concluded that the given function is not periodic.
  • #1
rafnhy
1
0
Hello, I have got a question about the periodicity of a function.
I know that in discrete domain, a periodic function have to verify
x[n] = x[n+N]
where N is the positive integer and foundamental period.
My problem is that if I have a function like this: e^(j3π(n+1/2)/5),
how can I confirm if that the function can be periodical?
I attemted to use the Euler equivalent, but still no solution came to my mind.
Thank you!
 
Engineering news on Phys.org
  • #2
I attached a photo.It's not so clear but I hope you can understand the content in it.According to that discussion,I found that given func. is not periodic.
 

Attachments

  • IMG0187A.jpg
    IMG0187A.jpg
    22.9 KB · Views: 417

1. What is periodicity in a function?

Periodicity in a function refers to the repeating pattern of the output values at regular intervals of the input values. In simpler terms, it is the characteristic of a function to have a predictable and repetitive behavior.

2. How do you check the periodicity of a function?

To check the periodicity of a function, you can plot the function on a graph and observe if it repeats itself at regular intervals. Another method is to use the period formula, which is the difference between two consecutive x-values that give the same output. If this value remains constant, the function is periodic.

3. Can a non-periodic function become periodic?

No, a non-periodic function cannot become periodic. Periodicity is a fundamental characteristic of a function, and it cannot change. However, certain non-periodic functions can exhibit periodic behavior in a specific interval or under certain conditions.

4. What is the difference between periodic and non-periodic functions?

The main difference between periodic and non-periodic functions is that periodic functions have a repeating pattern, while non-periodic functions do not. Periodic functions also have a constant period, while non-periodic functions do not exhibit any regularity or predictability in their output values.

5. How is periodicity useful in real-life applications?

Periodicity is useful in many fields, including physics, engineering, and finance. In physics, it is used to describe the behavior of waves and oscillations. In engineering, it helps in designing and analyzing systems with repetitive behavior, such as electrical circuits. In finance, periodicity is used to study the repeating patterns in stock market trends and make predictions.

Similar threads

I Orthogonal Basis of Periodic Functions: Beyond Sines and Cosines
    • Calculus
4
Replies
139
Views
4K
A Measure of non-periodicity of almost periodic functions
    • General Math
Replies
1
Views
1K
I What's the definition of "periodic extension of a function"?
    • Topology and Analysis
Replies
14
Views
3K
A Prove a series is periodic
    • General Math
Replies
33
Views
2K
B Can a function have two fundamental periods?
    • General Math
Replies
20
Views
2K
Specifying vertical asymptotes in periodic functions in set notation
    • Precalculus Mathematics Homework Help
Replies
3
Views
2K
Burst period on function generator
    • Electrical Engineering
Replies
7
Views
1K
Some questions about Fourier series
    • General Engineering
Replies
3
Views
2K
A Backward Euler technique vs. periodic function: Damping out?
    • Differential Equations
Replies
7
Views
2K
Fourier series, periodic function for a string free at each end
    • Introductory Physics Homework Help
Replies
8
Views
1K

Hot Threads

Recent Insights

Back
Top