Question

• Problem 2 (15 % of the total mark) For each of the following systems, determine whether or not the system is linear. Show your derivations. i) y(n) = \x(n − 1). ii) y(n) = x(n − 3). iii) y(n) = 2x(n) + sin (27(n)).

Answer 1

** a) absolute function is not linear

b) shifting is linear function

ii) y[m] = 1*(4-1)/ too linear, yox ) = y(x) 4 864) 311-1). Hlo) -1 260 0 -) Y()+ 4-) - 1x11-1) 1 + 1*(1-0)/ - 1x (0)| + 1*(-))) - o & © so y (n) is not linear. IMA ii) y = a [n-3] 1. y in shifting to be units Right side shibting in linear so y in limero fiii) y cn3 = 2 *[n] * Bine (n) for y[m3 to be linear, y can) = a g(x) y [an] = 2 x [an] + sina [an] - ay [n] = 2a8[n] +asina [n] - 0 y lang = a (z a [an] + Sinx (n)): a yin] so it in lineart function.