What is the error in this computation?
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Here I want to plot a simple sum.
I computed it manually by iterating different values, and then did it same by using for loop, but there is some mistake, can somebody figure it out for me.
Below given is my code:
x = 0:pi/16:pi;
s = (8/(pi*(1^3)))*sin(1*x)+...
(8/(pi*(3^3)))*sin(3*x)+...
(8/(pi*(5^3)))*sin(5*x)+...
(8/(pi*(7^3)))*sin(7*x)+...
(8/(pi*(9^3)))*sin(9*x)+...
(8/(pi*(11^3)))*sin(11*x)+...
(8/(pi*(13^3)))*sin(13*x)+...
(8/(pi*(15^3)))*sin(15*x);
ss = 0;
for k =1:16
ss = ss + (8/(pi*(k^3)))*sin(k*x);
end
plot(x,s,'b-',x,ss,'r-');
Why I choose odd values in manual sum because sin(k*pi) = 0, where k=2,4,... ,but i took all (even and odd) values in for loop
The plot generated is given below:
采纳的回答
Walter Roberson
2020-1-4
0 个投票
sin(k*pi) is 0 for integer k but you have sin(k*x) where x is a fraction of pi and that does not vanish.
3 个评论
Muhammad Usman
2020-1-4
Steven Lord
2020-1-4
In theory sin(k*pi) is 0 for integer k. In practice if you're computing sin(k*pi) consider using the sinpi function introduced in release R2018b.
sin(pi) % not exactly 0
sinpi(1) % exactly 0
Walter Roberson
2020-1-4
Using k=1:2:16 should duplicate your manual calculation.
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