partial sum of a series

i have this function and i wrote the following code to calculate the Fourier coefficients

im just stuck with writing a loop which calculate the partial sum of the series till a given number N as well as Plotting the function and the corresponding partial sum (N = 12) on one figure.

can any one help?

[Walter Roberson]

Please post actual code instead of pictures of code. We cannot feed pictures of code to MATLAB to execute, and we cannot (at all easily) edit pictures of code.

[SSBGH]

syms x
f = 1/2*(sin(x)+abs(sin(x)));
%%a0 
a0_sym= (1/pi)*int(f,x,-pi,pi);
a0= double(a0_sym)
%%an, bn
for n =1:12;
    a_sym(n) = (1/pi)*int(f*cos(n*x),x,-pi,pi);
    b_sym(n) = (1/pi)*int(f*sin(n*x),x,-pi,pi);
    
    a(n)=double(a_sym(n))
    b(n)=double(b_sym(n))
    
end

here you go

[Walter Roberson]

syms x
Pi = sym(pi);

f = 1/2*(sin(x) + abs(sin(x)))

f = 

X = linspace(-Pi, Pi);
F = double(subs(f, x, X));
plot(X, F)

fourier(f, x)

ans = 

f2 = piecewise(x >= 0 & x <= 3*Pi/2, sin(x), zeros(size(x)))

f2 = 

F2 = double(subs(f2, x, X));
plot(X, F2)

fourier(f2)

ans = 

sympref('HeavisideAtOrigin', 0);
f3 = (heaviside(x)-heaviside(x-3*Pi/2))*sin(x)

f3 = 

F3 = double(subs(f3, x, X));
plot(X, F3)

simplify(fourier(f3, x), 'steps', 10)

ans = 

Interesting, it appears that you can get a closed formula -- though you have to work at it a bit.

Answer 1

[Paul]

Hi SSBGH,

To plot the function, we need a set of x-values to plot over.

As you've done, define the function and the CFS coefficients symbolically

syms x
syms n integer positive % missing from original code!
f = 1/2*(sin(x)+abs(sin(x)));
%%a0 
% use sym(pi) when doing symbolic math
Pi = sym(pi);
a0_sym   = (1/Pi)*int(f,x,-Pi,Pi); % this equation has been corrected
a_sym(n) = (1/Pi)*int(f*cos(n*x),x,-Pi,Pi)

a_sym(n) = 

b_sym(n) = (1/Pi)*int(f*sin(n*x),x,-Pi,Pi)

b_sym(n) = 

Now define the values of x to make the plot

xvals = -pi:.01:pi;

Now we loop over the CFS coefficients to sum them all up over all values of x

N = 12;

% intialize with a0
fr = double(a0_sym)/2;

for n = 1:N;
    
    a = double(a_sym(n));
    b = double(b_sym(n));
    
    % at this point, fill in the RHS
    fr = fr + ... 
    
end

Now plot

plot(xvals,1/2*(sin(xvals) + abs(sin(xvals))),xvals,fr)