Wednesday

July 23, 2014

July 23, 2014

Posted by **Nicole** on Sunday, December 7, 2008 at 1:01pm.

I'm trying to find the Fourier Series of a function which is 1 from -pi/2 to pi/2, and zero everywhere else

inside of -pi to pi. I realize this is a square wave and I began the problem with a piecewise function

s(t) = 1 abs(t) < pi/2

0 abs(t) > pi/2

Then I had

a_k = 1/pi integral(from -pi to pi) of [cos(kt)dt]

and

b_k = 1/pi integral(from -pi to pi) of [sin(kt)dt]

but I don't know what to do from here.

Any help is greatly appreciated, thank you!

- Reiny Can't Help Here -
**Reiny**, Sunday, December 7, 2008 at 2:21pmThe last time I dealt with that topic was over 45 years ago, and frankly I don't feel confident enough to answer.

Perhaps some of the other math experts might want to take a crack at it if they are on.

- Linear Algebra -
**Damon**, Sunday, December 7, 2008 at 2:36pmThis is not a Fourier series really but a Fourier integral. The series would apply if the function were periodic.

However this function has to be zero from - oo to - pi/2

Then it jumps up one at -pi/2

Then it jumps down one at +pi/2

That is a unit step up at -pi/2

minus

A unit step up at + pi/2

- Linear Algebra -
**Damon**, Sunday, December 7, 2008 at 2:50pm

- Linear Algebra -
- Linear Algebra -
**Damon**, Sunday, December 7, 2008 at 6:19pmI think you were doing fine now that I look at what you did.

a_k = 1/pi integral(from -pi to pi) of [cos(kt)dt]

= 1/(k pi) [sin k pi - sin(-k pi)

= (2/k pi)sin k pi

which is the answer

and

b_k = 1/pi integral(from -pi to pi) of [sin(kt)dt]

= 1/(k pi) [-cos k pi + cos -k pi}

= 0 because cosine is even

**Related Questions**

Linear Algebra - Hello, I'm trying to find the Fourier Series of a function ...

Math (College Level Mathematics) - Fourier sin series for f(x) = 1, 0 < x <...

math - The Fourier series expansion for the periodic function,f(t) = |sin t|is ...

math - The Fourier series expansion for the periodic function,f(t) = |sin t|is ...

math - Anyone can help me on this qns? The Fourier series expansion for the ...

Fourier Series - A periodic function f(t), with period 2π is defined as,f(...

Math (Fourier) - I want to self-study Fourier Transforms followed by signal ...

Fourier Sine Series Q - I have the function f(x) = cos(x) on the interval from 0...

Algebra - Using the index of a series as the domain and the value of the series ...

calculus - Find the fourier series of F(x) = 1, -L<=x<0 = 0, 0<=<L f...