Calculate continuous Fourier Series for 50 coefficients

My code:

f = @(x) cos(3*x) - 0.5*sin(5*x) + 0.05*cos(54*x);
a0 = (1/pi)*integral(f,-pi,pi);
a50 = @(x) (1/pi)*integral(f*cos(50*x), -pi, pi);

for k = 1:1:49
    rk = @(x) (1/pi)*integral(f*cos(k*x),-pi,pi)*cos(k*x) + (1/pi)*integral(f*sin(k*x),-pi,pi)*sin(k*x);
    r = @(x) r + rk;
end

v = @(x) a0/2 + a50*cos(50*x) + r;

hold on
fplot(f, [-pi,pi], 'k')
fplot(v, [-pi,pi], 'r')

I am attempting to find the fourier series for f, as specified in my code. I am not an expereinced coder, and I believe I am calculating the Fourier coefficients incorrectly. When running the code, I get the following warnings:

Warning: Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your
function to return an output with the same size and shape as the input arguments. 
> In matlab.graphics.function.FunctionLine>getFunction
  In matlab.graphics.function.FunctionLine/updateFunction
  In matlab.graphics.function.FunctionLine/set.Function_I
  In matlab.graphics.function.FunctionLine/set.Function
  In matlab.graphics.function.FunctionLine
  In fplot>singleFplot (line 237)
  In fplot>@(f)singleFplot(cax,{f},limits,extraOpts,args) (line 192)
  In fplot>vectorizeFplot (line 192)
  In fplot (line 162)
  In Hw5 (line 15) 
Warning: Error updating FunctionLine.

 The following error was reported evaluating the function in FunctionLine update: Undefined function
 'mtimes' for input arguments of type 'function_handle'.
 
Warning: Error updating FunctionLine.

 The following error was reported evaluating the function in FunctionLine update: Undefined function
 'mtimes' for input arguments of type 'function_handle'.

From this, I only see the plot of f instead of v(x). v(x) is to be built by using the standard techniques of calculating Fourier coefficients. Any help is appreciated, thank you.

Answer 1

[Shubham Gupta]

Try this :

r = @(x)0;
f = @(x) cos(3*x) - 0.5*sin(5*x) + 0.05*cos(54*x);
a0 = (1/pi)*integral(f,-pi,pi);
a50 = @(x) (1/pi)*integral(@(x)f(x).*cos(50*x), -pi, pi);

for k = 1:1:49
rk = @(x) (1/pi)*integral(@(x)f(x).*cos(k*x),-pi,pi)*cos(k*x) + (1/pi)*integral(@(x)f(x).*sin(k*x),-pi,pi)*sin(k*x);
r = @(x) r(x) + rk(x);
end

v = @(x) a0/2 + a50(x)*cos(50*x) + r(x);
hold on
fplot(f, [-pi,pi], 'k')
fplot(v, [-pi,pi], 'r')

You should not multiply or add scalar to function handle.

I hope this helps !