This project considers the trigonometric interpolation and least square approximation.
For each of the following functions,
(a), f(t)=e⁻ᵗ²;
(b), f(t)=eᵗ.
and the interval -1,1. (i) Write a program to find the trigonometric interpolation function P(t) of orderN=8,16,32,64,128,256. The data points are,
(tn,f(tⱼ)),j=0,1,cdots,N-1.,tⱼ=-1+j(2/N). Plot the error curves of the interpolation function, by evaluating |P(t)-f(t)| at p=2048 evenly spaced points, using FFT.