How do I plot this Fourier series funcion?

Hello everyone,

I have tried to plot the function below from (0,pi) for a0 and the first six terms of the series on matlab. I did not know how to include the sin and cos function together so I tried to plot the cos term first, However, it seems like it does not work with the followig code becaue of (cos, sin) error. I would appriciate your help.

a0 = pi/4

an = 1/pi(cos(n*pi)-1)

bn = (-1*cos(n*pi))/n

f(t) = a0 + sum(an*cos(n*t))+ sum(bn*sin(n*t))

t = 0:0.1:2*pi;
n = 6;
ycos = cos(t,n);
plot(x,ycos),grid
xlabel('t'),ylabel('cos function')


% Define functions
function f = fcos(t,n)
         
         f = zeros(1,numel(t));
         f = pi/4;
         for i = 1:n
             an = -1/pi(cos(i*pi)-1) ;
             f = f + an*cos(i*t);
         end

Answer 1

[Star Strider]

I am not exactly certain what you want to do, however the loop is likely not necessary, sinc it is prefgerable to use MATLAB’s vectorisation capabilities —

t = 0:0.1:2*pi;
n = 1E-8+(0:6).';                                   % Adding 1E-8 Prevents NaN Values In The Output, Transposed To Column Vector
a0 = pi/4;
an = 1./(pi*(cos(n*pi)-1)) 

an = 7×1

1.0e+14 * -7.1677 -0.0000 -7.1677 -0.0000 -7.1677 -0.0000 -7.1677

bn = (-1*cos(n*pi))./n

bn = 7×1

1.0e+08 * -1.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000

f = @(t) a0 + sum(an.*cos(n.*t))+ sum(bn.*sin(n.*t));

figure
plot(t, f(t))
grid

Make appropriate changes to get different results.

.

[Hasan Al Tarify]

Thanks for your answer. In fact, I tried to get the same results as shown in the figure below so I can compare it to the periodic impulse response that I obtained. I hope you understand.

[Star Strider]

I do not exactly understand.

The resolution of the square waves can be increased by increasing ‘n’ and ‘t’ —

% t = 0:0.1:2*pi;
t = linspace(0, 6*pi, 500);
n = 1E-8+(0:16).';                                  % Adding 1E-8 Prevents NaN Values In The Output, Transposed To Column Vector
a0 = pi/4;
an = 1./(pi*(cos(n*pi)-1)) 

an = 17×1

1.0e+14 * -7.1677 -0.0000 -7.1677 -0.0000 -7.1677 -0.0000 -7.1677 -0.0000 -7.1677 -0.0000

bn = (-1*cos(n*pi))./n

bn = 17×1

1.0e+08 * -1.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000

f = @(t) a0 + sum(an.*cos(n.*t))+ sum(bn.*sin(n.*t));

figure
plot(t, f(t))
grid

Since a square wave pulse train is the sum of the scaled odd multiples of a sine curve, one way to create it is simply —

t = linspace(0, 2, 1500);
n = 1:2:16;
f = 2.5;
f = sum(sin(n(:)*2*pi*t*f)./n(:));

figure
plot(t, f)
grid

A cosine series is not necessary.

.

[Hasan Al Tarify]

Aha, I understand now. So I tried both codings but this is what appears on screen as an error.

Array indices must be positive integers or logical values.

[Star Strider]

They both ran without error for me. I have no idea what the problems is, since I cannot reproduce it.

The ‘t’ and ‘n’ vectors in the second plot are different from those in the first plot, so it is not possible to run both of them with the same ‘t’ and ‘n’ vectors. Run them separately (at least with the vectors created for them), and they should work correctly.

.

[Hasan Al Tarify]

Oh I have figured it out. There were old variables with different values of the same ones you entered. I solved it now. I really appriciate your help and patience.

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

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