I am stuck with the following problem: \begin{align} \max_{\theta\in\mathbb{R}}\sum_{i=1}^{N}(a_i\sin(i\theta)+b_i\cos(i\theta)), \end{align} where for $i(1\leq i\leq N$)$, a_i$ and $b_i$ are real numbers. If a solution is not known, please point to references which deals with this sort of equations.
Asked
Active
Viewed 69 times
0
-
http://math.stackexchange.com/questions/17966/how-can-we-sum-up-sin-and-cos-series-when-the-angles-are-in-arithmetic-pro – lab bhattacharjee Feb 26 '14 at 14:52
1 Answers
1
This is a trigonometric polynomial, or a finite instance of a Fourier series with period $2\pi$. There is nothing obvious that would help you to find the maximum, take the first derivative and look for its roots.
Lutz Lehmann
- 126,666
-
Also: it is periodic, so you only have to look in $[0,2\pi]$ for the maximum. – GEdgar Feb 26 '14 at 15:23