Fourier series odd and even functions

In summary, the conversation is about someone trying to understand the process of expanding a function into a Fourier series but not having enough information. They are also confused about why a sine term is being added to the last step. The other person suggests looking at the definition of a Fourier series for clarification.
  • #1
robertjford80
388
0

Homework Statement



Screenshot2012-06-17at55656AM.png





The Attempt at a Solution



I don't understand the step above. It has something to do with this equation

Screenshot2012-06-17at55946AM.png


I think. I'm supposed to expand it into an appropriate Fourier series.
 
Physics news on Phys.org
  • #2
You haven't given us enough information. What is f(x)? You were probably given a function and asked to expand it in a sine series.
 
  • #3
The "step above" is just applying the definition of the Fourier series:
Are you saying you do not know what that is?
 
  • #4
here is some more info

Screenshot2012-06-17at70852PM.png


Screenshot2012-06-17at70757PM.png


Screenshot2012-06-17at70808PM.png


I don't understand why they're adding the sin on to that last step.
 
  • #5
robertjford80 said:
I don't understand why they're adding the sin on to that last step.


What is the definition of a Fourier series?
 

1. What are Fourier series odd and even functions?

Fourier series odd and even functions are mathematical representations of periodic functions in terms of sine and cosine functions. Odd functions can be described as functions that are symmetric about the origin, while even functions are symmetric about the y-axis. Fourier series allows us to break down a periodic function into an infinite sum of these sine and cosine functions.

2. How do odd and even functions relate to Fourier series?

Odd and even functions are important in the study of Fourier series because they have special properties that allow us to simplify the calculations. For example, the Fourier coefficients for odd functions are equal to zero for the cosine terms, and the coefficients for even functions are equal to zero for the sine terms.

3. What is the difference between odd and even functions in Fourier series?

The main difference between odd and even functions in Fourier series is their symmetry. Odd functions have a point of symmetry at the origin, while even functions have a line of symmetry at the y-axis. This results in different coefficients for the sine and cosine terms in the Fourier series representation.

4. Can any periodic function be represented by a Fourier series of odd and even functions?

Yes, any periodic function can be represented by a Fourier series of odd and even functions. This is known as the Fourier series expansion, and it allows us to approximate any periodic function with a finite number of terms in the series.

5. What is the significance of odd and even functions in practical applications?

Odd and even functions have many practical applications, especially in signal processing and engineering. For example, odd functions are commonly used to represent alternating current signals, while even functions are used to represent direct current signals. Fourier series of odd and even functions also play a crucial role in the analysis and design of filters and amplifiers.

Similar threads

  • Calculus and Beyond Homework Help
Replies
3
Views
165
  • Calculus and Beyond Homework Help
Replies
3
Views
267
  • Calculus and Beyond Homework Help
Replies
6
Views
275
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
310
  • Calculus and Beyond Homework Help
Replies
1
Views
134
  • Calculus and Beyond Homework Help
Replies
6
Views
872
  • Calculus and Beyond Homework Help
Replies
2
Views
323
  • Calculus and Beyond Homework Help
Replies
1
Views
97
  • Calculus and Beyond Homework Help
Replies
4
Views
273
Back
Top