$\begingroup$

i am trying to plot the following Fourier series $x(t)$

t=0:0.01:2;
A = 10;
T = 2;
w0 = 2*pi/T;
N = 10;
xN = zeros(1,length(t)); % dc component
for n=1:N xN = xN + (1/(2*n-1)) * sin(2*n -1)*w0*t;
end
x = (4*A/pi) * xN;
plot(t,x)
xlabel('t')
ylabel('x(t)')

The result must be:

My code doesn't seem to be working, any help would be much appreciated, thank you.

$\endgroup$

3 Answers

$\begingroup$

You can always use the symbolic toolbox - I find it nicer for doing things such as computing Fourier Series. Example code below.

syms t n k
A = 10;
w_0 = pi;
%% Formula for the Fourier Series
fourierseries = @(t,k) 4*A/pi*symsum(sin((2*n-1)*pi*t)/(2*n-1),n,1,k);
%% Plot with 20 Fourier coefficients
ezplot(fourierseries(t,20),-2,4)
title('Fourier Series'), xlabel('t'), ylabel('f(x)');

$\endgroup$ 1 $\begingroup$

Your brackets are wrong. Correct would be (note the added brackets after sin)

for n=1:N xN = xN + (1/(2*n-1)) * sin( (2*n -1)*w0*t );
end

The code the way you wrote it is interpreted differently. In your code the argument of the sine function is only (2*n-1), which is a constant.

$\endgroup$ 0 $\begingroup$

You can create a function of the amplitude and frequency of the term inside the summation, depending only on n - the dummy variable.

Using the values you provided, you have:

A = 10;
T = 2;
w0 = 2*pi/T;
N = 10;

Now, the amplitude and frequency as function of the iterator n is:

a = @(n) 1./(2*n-1); % amplitude
w = @(n) (2*n-1)*w0; % frequency

Now, the (truncated) Fourier series may be give as:

xt = @(t,n) 4*A/pi*sum(a(1:n).*sin(w(1:n)*t)); % fourier series

This is a function of the number of terms n you want to include in your approximation of the infinite series and the also a number of the independent variable t.

If you want to create a plot of the function, you must create the independent variable array and the dependent variable array.

t = -2*T:T/100:T*2; % plots from -2T to 2T, with a step of T/100
x = 0*t; % pre-allocate for speed
for i=1:length(t) x(i) = xt(t(i),N); % calculates the value for each t(i) in the array t
end
figure
plot(t,x)

This code does not use any function from the symbolic toolbox that may not be available depending on your version of MATLAB.

$\endgroup$

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy