Consider an LTI system, initially at rest, described by the difference equation y(n) = y(n 2) + x(n) (a) Determine the impulse response, h(n),

Consider an LTI system, initially at rest, described by the difference equation

y(n) = ¼y(n – 2) + x(n)

(a) Determine the impulse response, h(n), of the system.

(b) What is the response of the system to the input signal

x(n) = [(1/2)ⁿ + (-1/2)ⁿ]u(n)

(c) Determine the direct form II, parallel-form, and cascade-form realization for this system.

(d) Sketch roughly the magnitude response |H(ω)| of this system.

in) b2 xin) Co in) 2-1 2 42 a,