Help with Matlab HW Problem

Okay, so I'm a beginner and I really need some help on a homework problem that I'm not understanding. I haven't gotten very far, so I apologize, but any guidance would be extremely appreciated. The task is this:

A Fourier series is an infinite series representation of a periodic function in terms of sines and cosines at a fundamental frequency (matching the period of the waveform) and multiples of that frequency. For example, consider a square wave function of period L, whose amplitude is 1 for 0 L/2, –1 for L/2 L, 1 for L 3L/2, and so forth. This function is plotted in Figure 5.15(the function is just a squarewave function). This function can be represented by the Fourier series f(x)= (sigma from i=1,3,5... to n) (1/n)*sin(n*pi*x)/L (5.15) Plot the original function assuming L=1, and calculate and plot Fourier series approximations to that function containing 3, 5, and 10 terms.

I know that we're supposed to create a fourier series with 3, 5, or 10 terms by implementing a for loop. My attempt at a solution goes something like this:

for ii = 1:2:5
    fourier_n = (1/ii)*sin(ii*pi*x);
end

In my head, I don't understand how that would NOT create the fourier series. However, MATLAB gives me this whenever I try to see my results: "Undefined function or variable 'x'." How else am I supposed to create a fourier series with a few terms if it won't allow me to include x in the terms? If I simply leave the 'x' out of the for loop, it will be incorrect because it will give a value for the expression when it should output a function instead. Any tips or help at all will be appreciated immensely. Thank you!

Answer 1

[Image Analyst]

You need to define x before the loop, like if you want x to go between -2*pi and 2*pi in 500 steps:

x = linspace(-2*pi, 2*pi, 500);

[Juan]

ok, so I included what you suggested and it did get rid of the error message. however, the plot is not a square wave. the plot is a sin wave, which makes me think that it's simply plotting the final value for fourier_n which would would essentially be (1/5)*sin(5*pi*x)... what i'm looking for is a function in the form of f1(x)+f3(x)+f5(x)... my initial thought is to make a recursive sum within the for loop and then plot that final value... how would i go about doing this? thank you!

[Matt Kindig]

The sum idea is the way to go:

fourier_n = zeros(size(x));  %initialize fourier_n to zeros

for ii = 1:2:5
    fourier_n = fourier_n + (1/ii)*sin(ii*pi*x);   %add next term
end

[Juan]

thank you so much. it works perfectly now. you guys are awesome

[Image Analyst]

You're welcome. I think you were supposed to observe that as you include more and more terms (ending value goes from 5 to 9 to 15 or 31....) that the shape gets closer and closer to a square wave. Please mark answer as Accepted if we're done now.

[Image Analyst]

Please mark answer as Accepted if we're done now.