Question: Consider the following difference equation: y[n] y[n 1] 1/8 y[n 2] = 3x[n]. (a) Determine the general form of the

Consider the following difference equation:

y[n] – ¼ y[n – 1] – 1/8 y[n – 2] = 3x[n].

(a) Determine the general form of the homogeneous solution to this difference equation.

(b) Both a causal and an anti causal LTI system are characterized by this difference equation. Find the impulse responses of the two systems.

(c) Show that the causal LTI system is stable and the anti causal LTI system is unstable.

(d) Find a particular solution to the difference equation when x[n] = (1/2)nu[n].

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