Problem 1 (10 pts). Consider two 1D sequences x(n) with 10 elements and h(n) with 3 elements. Further, the sequence x(n) can be also denoted by the vector x of length 10. Find a matrix H such that the product = Hx is identical to the correlation between x(n) and h(n), i.e. y(n) = X2, h(k +n 1) x(k). 1. 2pts: What are the dimensions of H assuming that we are interested in values y(n) for which of all samples of h(n) are overlapping with samples of x(n)? 2. 1 pt: What 1s the size of the output vector y? 3. 6 pts: What are the dimensions of H for the 2D case where x(m,n) 1s a 10 x 10 image, and h(m, n) 1s a 3x3 kernel, and the output is given by y(m,n) = X X h(j + m 1,k + n 1)x(j, k)? Assume that we are only considering the values of y(m, n) obtained when h(m, n) is fully overlapped with x(m, n). What is the size of y in this case? 4. 1 pt: What can you say about the structure of the matnx H