Solution Found!
Find the trigonometric polynomial F(x) of the form (2) for which the square error with respect to the given f(x) on the interval \(-\pi<x<\pi\) is minimum. Compute the minimum value for \(N=1,2, \cdots, 5\) (or also for larger values if you have a CAS). \(f(x)=\left\{\begin{array}{rlr}-1 & \text { if } & -\pi<x<0 \\ 1 & \text { if } & 0<x<\pi\end{array}\right\).
Chapter 11, Problem 5(choose chapter or problem)
Find the trigonometric polynomial of the form (2) for which the square error with respect to the given on the interval \( - \pi < x < \pi \) is minimum. Compute the minimum value for \(N = 1,2, \cdots ,5\) (or also for larger values if you have a CAS).
\(f(x)=\left\{\begin{array}{rlr}-1 & \text { if } & -\pi<x<0 \\1 & \text { if } & 0<x<\pi\end{array}\right.\)
Questions & Answers
QUESTION:
Find the trigonometric polynomial of the form (2) for which the square error with respect to the given on the interval \( - \pi < x < \pi \) is minimum. Compute the minimum value for \(N = 1,2, \cdots ,5\) (or also for larger values if you have a CAS).
\(f(x)=\left\{\begin{array}{rlr}-1 & \text { if } & -\pi<x<0 \\1 & \text { if } & 0<x<\pi\end{array}\right.\)
ANSWER:Step 1 of 6
Given:- The polynomial \(f\left( x \right) = \left\{ \begin{array}{l} - 1{\rm{ if }} - \pi < x < 0\\1{\rm{ if }}0 < x < \pi \end{array} \right.\).