Ex. 5.6

Ex. 5.6

Suppose you wish to fit a periodic function, with a known period \(T\). Describe how you could modify the truncated power series basis to achieve this goal.

Soln. 5.6

If the period \(T\) is known, without loss of generality, the problem reduces to use truncated power series on domain \([0, T]\). For \(x\in \mathbb{R}\), it's easy to map it to \(x^\ast\in [0,T]\) such that \(f(x) = f(x^\ast)\).

Alternatively, we could consider Fourier basis for periodic function.