Calculating Fourier Series for an Odd Function

In summary, the given function f(t) can be expressed using the Fourier Series with the general formulas for the coefficients, both a and b, as it is neither odd nor even.
  • #1
ganondorf29
54
0

Homework Statement



f(t) is given as:

from 0 to 0.2s, f(t) = 5
from 0.2s to 0.6s, f(t) = 0
from 0.6s to 0.8s, f(t) = 5,
etc

Homework Equations


for an odd function

a0 = 2/p * integral(from -p/2 to p/2) of f(t) dt

bn = 4/p * integral(from 0 to p/2) of f(t)*sin(2*pi*n*t/p) dt

The Attempt at a Solution



The problem is that since the function is "off" for a longer period than it is "on"; I'm not sure how to incorporate that into the Fourier Series, especially the bn term
 
Physics news on Phys.org
  • #2
The function f(t) is neither odd nor even, so you have to use the general formulas for the coefficients, both the a's and b's.
 

FAQ: Calculating Fourier Series for an Odd Function

1. How do you determine if a function is odd?

A function is considered odd if it satisfies the property f(-x) = -f(x) for all values of x. This means that the function is symmetric about the origin and has rotational symmetry of 180 degrees.

2. What is the formula for calculating the Fourier series of an odd function?

The formula for calculating the Fourier series of an odd function is: f(x) = (a0/2) + Σ(ank * sin(nπx/L)), where L is the period of the function and ank is the n-th Fourier coefficient.

3. Can an odd function have a constant term in its Fourier series?

No, since a constant term would violate the property of an odd function f(-x) = -f(x). Therefore, the Fourier series of an odd function will always start with a sin term.

4. Is it possible to have negative values for the n-th Fourier coefficient of an odd function?

Yes, it is possible to have negative values for the n-th Fourier coefficient of an odd function. This is because the sign of the coefficient depends on the function being approximated and the choice of the interval. However, the overall series will still be odd, since the negative sign will be canceled out by the sin term.

5. Can the Fourier series of an odd function converge to a non-odd function?

No, the Fourier series of an odd function will always converge to an odd function. This is because the coefficients and the terms in the series are all odd, so the resulting function will also be odd.

Similar threads

Replies
2
Views
1K
Replies
1
Views
962
Replies
4
Views
636
Replies
3
Views
948
Replies
6
Views
2K
Back
Top