fourier series code in matlab

Sir/Mdm i had a fourier equation need to be evaluate to find THD using matlab code but i am not able to solve this summation using matlab. The required equation which is to be evaluated given below.

and the values of cos angles are

9,20,40,60.

The code i had tried is:

clc;

syms p;

k=symsum(((cosd((2*p-1)*10))/(2*p-1)+(cosd((2*p-1)*22))/(2*p-1)+(cosd((2*p-1)*40))/(2*p-1)+(cosd((2*p-1)*61))/(2*p-1))^2,p,1,50);

j=sqrt(k)/3.14;

double(j)

I am always getting 1 as a solution please help to solve this.

Answer 1

[Ameer Hamza]

The solution estimated in your question seems correct. The following shows a numerical solution. Since the series is converging so, I used 100000 terms. You can check that increasing terms have no significant effect on the final sum.

angles = [9, 20, 40, 60];

s1 = @(k) sum(cosd(angles(:).*k(:).'))./k;
s2 = sqrt(sum(s1(3:2:100000).^2));
den = sum(cosd(angles));

result = s2/den;

Result:

result =
   0.097311482007934

[omkari sai krishna]

Thank you sir for your help. I am also getting the same answer if i tried for 10. I not able to understand where i had done mistake

[omkari sai krishna]

i had seen some of the research papers they had given a numeric solution other than 1 .

[Ameer Hamza]

They might be using a different equation. This equation seems to be always converging to some value near 1.

[omkari sai krishna]

okay sir i will check it. Thank you for your support sir. It really heps me a lot.

[Ameer Hamza]

I am glad to be of help.

[omkari sai krishna]

sir is my approach of code to this question is right or wrong?

[Ameer Hamza]

Please check my updated answer. I found that there was a mistake. Now it gives different values.

[Ameer Hamza]

You code, also seems correct. Start the sum k limits from 2 instead of 1

clc;
syms  p;
k=symsum(((cosd((2*p-1)*10))/(2*p-1)+(cosd((2*p-1)*22))/(2*p-1)+(cosd((2*p-1)*40))/ ...
    (2*p-1)+(cosd((2*p-1)*61))/(2*p-1))^2,p,2,50);
                                           %^ use 2 here
j=sqrt(k)/3.14;
double(j)