Assume a one-dimensional image (or signal) f = [1 4 6 8 75 3], (at points i = 1, ..., 7). a) Explain what linear interpolation means. Sketch the linear interpolation Fin(x) of f for 1 x 7. Is Flin (2) continuous? Is Flin (2) differentiable? b) The interpolation can be expressed using the following equation 7 g(x) = Fg(x) = g(x-i)f(i). = where the function g(x) is different for different types of interpolation. Which function g(x) correspond to linear interpolation? c) Let g(x) be defined as i=1 |-|2| if || 1, -2x10x2 16x+8 if 1 < x 2, if x > 2. (1) - Plot g(x), -3 x 3. Plot the interpolation F(x) of the function f using this g(x) for 1 x 7 (e.g. using Matlab for the calculations). Is F(x) continuous? Is F,(z) differentiable? (Here you need to have an argument that is better than you can see it in the graph").