Properties of Convolution (40 points) The 1D convolution between two signals f, g RN is defined as: (f g)[n] = N 1X k=0 f [n k]g[k]. (1) In this problem, you will derive properties of convolution and submit a PDF file of the answers to Grade- scope. 1.1 Matrix Formulation (10 points) Construct a matrix multiplication that produces the same result as a 1D convolution with a given filter. In other words, given a filter f , construct a matrix H such that f g = Hg for any input g. Here Hg denotes matrix multiplication between the matrix H and vector g