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Refer formulas below

Linear and Time-Invariant (LTI) Systems Discrete Time . y = x[n] * h Ex Max [kjh[n - k] . Distributive Property r[n] . (h,[n] + holm]) = x[n] * h,[n] + x[n] * hy[n] . H(w) = [ h(tje ted = [H(w)|4#() frequency response of H (Fourier transform of h(@) . y(t) = h(t) . x(t) = [* h(t -)x(r)dr = [> h(r)x(t - r)dr = h(t) * x(t) . Hetut] = H(wjejut . Y(w) = X(W) H(w) Block Diagrams action 1: multiply by a Delay action 2: delay one tick combinator: add inputs END OF FORMULASQuestion 5: For the LTI discrete-time system shown below: 1/3 x[n] Unit z[n] delay * y[n] 1/3 (a) (2 marks) Find the difference equation from input on] to output =[n] (ignore y[n] for this). (b) (5 marks) Find the impulse response h(n] from input r[a] to output =. (c) (10 marks) Find the overall impulse response bran from input [a] to output y[a]