Plotting the Fourier series in Matlab

In summary, the conversation discusses a problem related to a mathematical function and the use of MATLAB to obtain three figures. The speaker asks for help and clarifies if the person they are talking to has any prior experience with programming. They also mention the importance of using the documentation provided by the creators of the software.
  • #1
miss_t
1
0
I am very confused on how to start this problem, would highly appreciate some help!
Consider the function
f(x)=   0, -1≤x≤0
2x, 0≤x≤1.

The Fourier series coefficients for this function are given by [a][/0]=0.5, and for  k=1, 2, 3,...
 
[a][/k]=(2((-1)^k-1))/(k∏)^2 and [/k]=(2(-1)^(k+1))/k∏
.
Write a Matlab program to obtain three Figures:
(a) Figure 1 must contain a plot of the function f(x).
(b) Figure 2 must contain four subplots, arranged in a 2 X 2 grid. Each subplot must contain a plot of ,[g][/N](x)
one for each value of N= 1, 3, 7, 20.
(c) Figure 3 must contain a plot of f(x), and ,[g][/N](x) for N=  1, 3, 7, 20, all superimposed. Use a suitable
legend to identify the five plots in the figure.
In each case, make sure you use a suitable title, and labels for the axes. Pick at least 100 points from the interval
[-1, 10] so that you get a smooth looking plot.
 
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  • #2
Hey miss_t and welcome to the forums.

This looks like a class problem, so I'll ask you what information have you been given in terms of the MATLAB functions.

Have you been given a reference guide by your tutors/lecturers? How much programming experience do you have whether its using C or something like MATLAB/Maple/Mathematica or some other mathematics computer package?

Basically what happens commonly is that the package creators provide documentation and help on all the commands that you can use as well as the parameters and then you just read the help file and do what you need to do, but if you haven't had any kind of programming experience this may seem daunting.
 

1. What is the Fourier series and why is it important?

The Fourier series is a mathematical technique used to represent any periodic function as a combination of sine and cosine functions. It is important because it allows us to analyze and understand complex periodic signals in terms of simpler components, making it useful in a wide range of fields such as signal processing, image processing, and quantum mechanics.

2. How do I plot the Fourier series in Matlab?

To plot the Fourier series of a periodic function in Matlab, you first need to define the function using the "syms" function and specify the period using the "period" function. Then, use the "fourierSeries" function to calculate the Fourier coefficients and the "fourierSeriesPlot" function to plot the series. You can also use the "stem" function to plot the coefficients.

3. Can I customize the plot of the Fourier series in Matlab?

Yes, you can customize the plot of the Fourier series in Matlab by using various functions such as "xlim" to specify the x-axis limits, "title" to add a title, and "xlabel" and "ylabel" to label the axes. You can also change the color, line style, and markers of the plot using the "plot" function.

4. How do I interpret the plot of the Fourier series in Matlab?

The plot of the Fourier series in Matlab shows the original function (in blue) and the Fourier series approximation (in red). The closer the two lines are, the better the approximation. The plot also displays the different frequency components of the original function, with the lowest frequency at the center and higher frequencies towards the edges.

5. Can I use the Fourier series to reconstruct the original function?

Yes, the Fourier series can be used to reconstruct the original function by adding up the individual sine and cosine functions with their corresponding coefficients. However, the accuracy of the reconstruction depends on the number of terms used in the series. A larger number of terms will result in a more accurate reconstruction.

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