Sketch illustrating the difference between a typical spectrum and a spectrum represented by a linear combination of basis functions. Top panel: typical spectrum, consisting of sampled flux values on a wavelength grid (black symbols) derived from the spectral photon distribution (red line). Central panel: coefficients representing the same data set by a linear combination of basis functions. Black symbols show the noisy representation, red dots the true coefficients. Bottom panel: linear combination of basis functions (black line) and the 1-σ error interval (grey shaded region) as a function of wavelength.