Fourier series equation for a even square wave

Jensen-
Messages
2
Reaction score
0
Can someone please help me with a Fourier series equation for a even square wave shown below:

F(t) = 0 when -2ms <t < -1ms
k when -1ms <t < 1ms
0 when 1ms <t < 2ms T=4

Im after finding the first 10 harmonic components. To be honest struggling with this one integration is not my strong point.
 
Physics news on Phys.org
Show us some work and what integral you are stuck on.
 
Hello, sorry for the late reply. I believe I have succesfully found Ao in my equation but An I am struggling with. I have attached my workings out if you may take a look it would be much appreciated.
 

Attachments

  • Fourier series - finding An.jpg
    Fourier series - finding An.jpg
    10.3 KB · Views: 574
  • fourier series - finding Ao.jpg
    fourier series - finding Ao.jpg
    7.2 KB · Views: 575

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Fourier series of this scale and shift of triangle wave
Replies
1
Views
1K
A few questions to make sure I understand Fourier series
Replies
3
Views
2K
How should I show that solutions can be expressed as a Fourier series?
Replies
3
Views
1K
Fourier transform of wave packet
Replies
3
Views
1K
Fourier series of translated function
Replies
1
Views
1K
Fourier series for trigonometric absolute value function
Replies
8
Views
3K
Show uniqueness in Dirichlet problem in unit disk
Replies
6
Views
1K
On pointwise convergence of Fourier series
Replies
3
Views
2K
Fourier Series for a Square-wave Function
Replies
2
Views
3K
Fourier Series of Sawtooth Wave from Inverse FT
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top