Numerical Methods with Programming

Modify Example 25.4.2 to create and plot two real trigonometric polynomials \(p\) such that the values \(p(0), p(1/9), \dots, p(8/9)\) are the 9 digits of your SUID number. One polynomial should use the aliased reconstruction formula k = [0:(n-1)/2 (1-n)/2:-1]; and the other the non-aliased formula k = 0:n-1.

The command subplot can help display these polynomials in one figure, for example subplot(2, 1, 1) before the first plot and then subplot(2, 1, 2) before the second. Which polynomial creates a more natural curve through given points?

Choose some complex numbers \(z_0, z_1, \dots, z_{n-1}\) (with odd \(n\)) so that connecting them in this order (and connecting \(z_{n-1}\) to \(z_0\)) one gets a closed curve similar to letter B. Then use Discrete Fourier Transform to plot a complex trigonometric polynomial interpolating these numbers (Example 25.4.1 may be helpful). Does the plot look like letter B?