ONLY A-C PLEASE An LTI system is given by the block-diagram below:+1x(n)NN-1(++)y(n)a)Write the difference equation that corresponds to the system and the impulse response of thesystem h(n)b) What is the frequency response H(w) of the system? (simplify as much as possible - hint: usesymmetry)c) Write the expression for the magnitude |H(w). What is the phase response ZH(w)?d) What discrete frequency/frequencies are completely blocked by this system?e) If the input is a complex sinusoid x(n) = ejwon, where wo, what is the output of the systemy(n)? What is the output when wo = 7 Hint: use |H(w)|, ZH(w)f)i. Assume you are given a function H(z) as a ratio of 2 polynomials in z - how could you tell ifthis is a low-pass/high-pass or a band-pass filter? ii. Assume you are given some H (w) (this time,assume also you can access python/matlab or some other numerical software) - how could youquickly tell if H (w) represents a low-pass/high-pass or a band-pass filter? Explain both casesbriefly in no more than 2-3 sentences

Given: Block diagram of an LTI system, To find: a) Difference equation and impulse response, b) Frequency response, c) expressions for Magnitude |H(w)| and phase ∠H(w).a) Difference equation, y(n)=x(n)-x(n-2) Taking DTFT of above equation, Y(ω)=X(ω)-e-j2ωXω,⇒Y(ω)=X(ω)1-e-j2ω,⇒Y(ω)X(ω)=1-e-j2ω,⇒H(ω)=1-e-j2ω----Transfer function, Taking IDTFT of H(w), Impulse response, h(n)=δ(n)-δ(n-2) b) From step b), Hω=1-e-j2ω,⇒Hω=1-e-jωejω=ejω-e-jωejω,⇒Hω=2j e-jωejω-e-jω2j,⇒H(ω)=2j e-jω sin(ω),----Transfer function c) Expression of Magnitude response, |H(ω)|=2sin(ω), Expression of Phase response, ∠H(ω)=90-ω.