Converting f(x) to MATLAB Code for Fourier Series with n=500

In summary, the problem involves converting a piecewise function into Matlab code and creating a graph of the Fourier series with n=500. The poster has already done it analytically for n=2 but is seeking help for the larger n value. The function is periodic with period pi and there is no reason why it cannot be integrated by hand for any n. A link has been provided for further assistance.
  • #1
zuelhuzz
1
0
The problem are as below :-

f(x) = {
x, for 0 < x < pi/2;
x/2, for pi/2 < x < pi;
pi-(x/2), for pi < x < 2*pi;

how do I convert it to Matlab code and produce a graph of Fourier series with n=500?

I have done analytically by hand for n=2, but the question ask to produce n=500, can anybody help?
 
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  • #2
I don't see any reason why that can't be integrated, "by hand", for any n. It doesn't look like the general n would be any harder than n= 1 or 2. Are we to assume this is periodic with period pi?
 

1. What is Fourier Series and how is it used in MATLAB?

Fourier Series is a mathematical technique used to represent a periodic function as a sum of sinusoidal functions. In MATLAB, it is used to analyze and manipulate signals and data that have periodic components.

2. How do I generate a Fourier Series plot in MATLAB?

To generate a Fourier Series plot in MATLAB, you can use the "plot" function after defining the appropriate variables and parameters for your function. You can also use the "stem" function for a more accurate representation of the Fourier Series plot.

3. Can I use Fourier Series to analyze non-periodic functions?

No, Fourier Series is only applicable to functions that are periodic. To analyze non-periodic functions, you can use other techniques such as the Fourier Transform.

4. How do I determine the number of terms to use in a Fourier Series?

The number of terms in a Fourier Series is determined by the highest frequency component in the signal. You can use the Nyquist-Shannon sampling theorem to determine the minimum number of terms needed for a good approximation. In MATLAB, you can also use the "fft" function to automatically determine the number of terms needed.

5. Are there any built-in functions in MATLAB for Fourier Series?

Yes, MATLAB has several built-in functions for Fourier Series such as "fft" for computing the discrete Fourier transform, "ifft" for computing the inverse Fourier transform, and "fft2" for computing the 2-dimensional Fourier transform. There are also other functions for specific applications, such as "filter" for filtering signals using Fourier Series.

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