3. Consider signals r(t) = t[u(t+1)u(t-1)] and y(t) = u(t+1)+2u(t)-u(t-1). For this problem, define the inner product between x(t) and y(t) as (a) Accurately plot x(t) and y(t). x(t)y" (t) dt. (x(t), y(t)) = | 2( (b) Find the best approximation of x(t) using y(t). That is, find cy in (t) = cyy(t) to minimize the error signal energy. Plot (t) and x(t) on the same graph. (c) Plot the error signal ex(t) = x(t)-(t). Determine the energy of the error signal E... Show that the error signal is orthogonal to y(t). (d) Find the best approximation of y(t) using x(t). That is, find c, in ŷ(t) = x(t) to minimize the error signal energy. Plot ŷ(t) and y(t) on the same graph. (e) Plot the error signal e,(t) = y(t) -ŷ(t). Determine the energy of the error signal E.,. Show that the error signal is orthogonal to x(t). (f) Would any of your previous answers change if the inner product was defined as an integral from -2 to 2? Would any of your previous answer change if the inner product was defined as an integral from -0.5 to 0.5? It is not necessary to redo all of your previous calculations if you carefully and fully explain your answers.