Two methods of denoising are mean filtering and median filtering: y_mean [n, m] = 1/r^2 sigma^[r/2]_i = -[r/2] sigma^[r/2]_j = -[r/2] x[n - i, m - j], y_median [n, m] = median{x[n - i, m - j]}, i, j = -[r/2], ..., [r/2], r elementof Z_+ (a) Describe what the mean filter does in your own words. Prove that it is LTI, and find an expression for the impulse response h[n, m]. Note that the impulse response is separable - find expressions for h_1 [n] and h_2[m] such that h[n, m] = h_1[n]h_2[m]. (b) Describe what the median filter does in your own words, and prove that it is time-invariant, but not linear