Fourier Series and Harmonics

f(x) = 2 between -2<x<0 and f(x) = 2-x between 0<x<2

f(x) = f(x+4)

Q) a) Find the coefficients of the first 5 harmonics. b) Plot the function and its approximating 5 term fourier series c) Sketch the fourier series (not the 5 term approximation) over the interval -6=<x=<6.

Can anyone help me with the above question or point me to an example of a similar fourier series question?

I do have the fnc M-file. I have entered the following:

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function result=fnc(x)

result=(x+4)

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I also believe that my L value is 2 and the n value is 5. I then need to enter fourier('fnc',L,n,'yes')

Is this correct?

Answer 1

[Star Strider]

I’m not exactly sure what you need to do, but this should get you started:

syms x w 

f1a = symfun(2, x);                         % Function Of ‘x’
f1b = symfun(2 - x, x);                     % Function Of ‘x’

Ff1a = int(f1a*exp(1i*w*n*x), x, -2, 0);    % Fourier Series
Ff1b = int(f1b*exp(1i*w*n*x), x,  0, 2);    % Fourier Series

Ff1 = simplify(Ff1a+Ff1b);                  % Combine For Complete Transform

You need to evaluate the functions and take their transforms piecewise, then sum them to get the complete transform. I defined ‘f1a’ and ‘f1b’ as functions here to make it easier for you to evaluate them at (x+4). You will have to use the subs function to evaluate them at their various harmonics (integer values of ‘n’).