Plotting a symbolic Fourier series

Question

I've written code for a Fourier series. This is what I have so far:

function FS = FourierSeries(f,degree)

cosCoefficients = zeros(1,degree);
sinCoefficients = zeros(1,degree);

syms x;

a0 = double((1/pi)*int(f,-pi,pi));


for n = 1:degree
    cosCoefficients = cosCoefficients + (1/pi)*int(f*cos(n*x),-pi,pi);
    sinCoefficients = sinCoefficients + (1/pi)*int(f*sin(n*x),-pi,pi);
end

for n = 1:degree
    FS = 0.5*a0 + cosCoefficients.*cos(n*x) + sinCoefficients.*sin(n*x);
end

Then, I've also created the following function file:

function y = func1(x)
syms x
y = (x^2);
end

The problem is that when I try to plot func1 and FS1 = FourierSeries(func1, 4), I keep getting an error that says

Data must be numeric, datetime, duration or an array convertible to double.

How do I plot this Fourier series?

Answer 1

whos FS1
  Name      Size            Bytes  Class    Attributes

  FS1       1x4                 8  sym   

This tells you that FS1 is a symbolic function, which needs to be evaluated before you can plot it:

FS1 = FourierSeries(func1, 4);
xIDX = -10:0.1:10;
array = zeros(size(xIDX));

for ii = 1:numel(xIDX)
    x = xIDX(ii);
    array(ii) = sum(double(subs(FS1)));
end

figure
plot(array)

subs converts your symbolic expression to a string, provided that the symbolic variable, x in this case, is present in the workspace. double then converts the string to an actual number, and since there's 4 terms in FS, we need to sum those, that's what a Fourier series is after all.

Even shorter, don't evaluate it numerically, but make use of MATLAB's built-in symbolic plot function fplot

figure
hold on
fplot(func1,'b')
fplot(sum(FS1),'r') % sum over the Fourier components
legend ('func1', 'FS1')