Illustration of the different steps of construction of the response function for BP. The blue line and shaded region is the initial guess, and the black line and grey shaded region is the true passband. The red line is the approximation using Eq. (22) and the green line the combination of the initial guess and the approximation with Eq. (22). The orange line shows the solution obtained with Eq. (48). The B-spline basis functions B_k(λ) are shown for comparison at the bottom of the plot.