Fourier series equation for a even square wave

In summary, the conversation is about a request for help with finding the Fourier series equation for an even square wave, with a period of 4 milliseconds and a given function. The person is struggling with finding the first 10 harmonic components and is asking for someone to show their work and help with the integral they are stuck on. They have also attached their workings out for reference.
  • #1
Jensen-
2
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.
 
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  • #2
Show us some work and what integral you are stuck on.
 
  • #3
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
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  • fourier series - finding Ao.jpg
    fourier series - finding Ao.jpg
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1. What is a Fourier series equation?

A Fourier series equation is a mathematical representation of a periodic function as a sum of sinusoidal functions. It is used to analyze and approximate any periodic function, including an even square wave.

2. What is an even square wave?

An even square wave is a type of periodic function that has a constant amplitude of 1 and a period of 2π. It is an even function, meaning that it is symmetric about the y-axis, and its values alternate between 1 and -1.

3. How is a Fourier series equation used to represent an even square wave?

A Fourier series equation for an even square wave can be written as f(x) = 4/π * (sinx + (1/3)sin3x + (1/5)sin5x + ...), where the summation continues for all odd values of n. This equation represents the even square wave by summing up an infinite series of sine waves with different frequencies and amplitudes.

4. What is the significance of the Fourier coefficients in the even square wave equation?

The Fourier coefficients represent the amplitudes of the individual sinusoidal functions in the Fourier series equation. In the case of an even square wave, the coefficients are all positive and decrease as the frequency of the sine wave increases.

5. Can a Fourier series equation accurately represent any periodic function?

Yes, a Fourier series equation can accurately represent any periodic function, including an even square wave. However, the accuracy of the representation depends on the number of terms included in the equation. As more terms are added, the approximation becomes closer to the actual function.

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