Let f(x) = x(2 - x) be sampled on n = 128 equally spaced points between 0 and 2 . Use a random number generator

Let f(x) = x(2π - x) be sampled on n = 128 equally spaced points between 0 and 2π . Use a random number generator with - 1 < rj < 1 to add noise by replacing each sample value fj = f(xj) by gj = fj + εrj. Investigate, for different values of ε, how many discrete Fourier modes are required to reconstruct a reasonable denoised approximation to the original signal.