This problem considers extension of interpolation using LUTs to two dimensions. Here we will use a known function that we can sample, then interpolate and measure the error. Let our system device be defined on the unit square [0, 1][0, 1] by

a) Create a 2-D, 4-bit look-up table (LUT) in each dimension, i.e., an equally spaced 16 16 grid, using bilinear interpolation to represent the function f (x, y).

(c) Using the approximation, find the mean square error on an equally spaced 1024 1024 grid.

(d) Create a 2-D 6-bit look-up table (LUT) in each dimension, i.e., an equally spaced 64 64 grid, using bilinear interpolation.

(e) Using the approximation, find the mean square error on an equally spaced 1024 1024 grid. Compare the results with the 4-bit LUT of step (a).

(f) Repeat the above using a nonlinear interpolation method of your choice.