The convolution sum of a finite sequence x[n] with the impulse response h[n] of an FIR system can be written in a matrix form y = Hx where H is a matrix, x and y are input and output values. Let h[n] = (1/3) (δ[n] + δ[n − 1] + δ[n − 2]) and x[n] = 2δ[n] + δ[n − 1].

(a) Write the matrix equation and compute the values of y[n].

(b) Use the DFT matrix representation Y = Fy, replace y to obtain an  expression in terms of Hand x. Use the DFT matrix representation  X = Fx and the orthogonality properties of F to obtain an expression in the DFT domain for the convolution sum.